29.6: The Wave Nature of Matter
Learning Objectives
By the end of this section, you will be able to:
- Describe the Davisson-Germer experiment, and explain how it provides evidence for the wave nature of electrons.
In 1923 a French physics graduate student named Prince Louis-Victor de Broglie (1892–1987) made a radical proposal based on the hope that nature is symmetric. If EM radiation has both particle and wave properties, then nature would be symmetric if matter also had both particle and wave properties. If what we once thought of as an unequivocal wave (EM radiation) is also a particle, then what we think of as an unequivocal particle (matter) may also be a wave. De Broglie’s suggestion, made as part of his doctoral thesis, was so radical that it was greeted with some skepticism. A copy of his thesis was sent to Einstein, who said it was not only probably correct, but that it might be of fundamental importance. With the support of Einstein and a few other prominent physicists, de Broglie was awarded his doctorate.
De Broglie took both relativity and quantum mechanics into account to develop the proposal that all particles have a wavelength , given by
\[\lambda = \dfrac{h}{p} \, (\text{matter and photons}),\]
where \(h\) Planck’s constant and \(p\) is momentum. This is defined to be the de Broglie wavelength . (Note that we already have this for photons, from the equation \(p = h/\lambda\).) The hallmark of a wave is interference. If matter is a wave, then it must exhibit constructive and destructive interference. Why isn’t this ordinarily observed? The answer is that in order to see significant interference effects, a wave must interact with an object about the same size as its wavelength. Since \(h\) is very small, \(\lambda\) is also small, especially for macroscopic objects. A 3-kg bowling ball moving at 10 m/s, for example, has
\[\begin{align*} \lambda &= h/p \\[4pt] &= (6.63 \times 10^{-34} \, J \cdot s)/[(3 \, kg)(10 \, m/s)] \\[4pt] &= 2 \times 10^{-35} \, m. \end{align*}\]
This means that to see its wave characteristics, the bowling ball would have to interact with something about \(10^{-35} \, m\) in size—far smaller than anything known. When waves interact with objects much larger than their wavelength, they show negligible interference effects and move in straight lines (such as light rays in geometric optics). To get easily observed interference effects from particles of matter, the longest wavelength and hence smallest mass possible would be useful. Therefore, this effect was first observed with electrons.
American physicists Clinton J. Davisson and Lester H. Germer in 1925 and, independently, British physicist G. P. Thomson (son of J. J. Thomson, discoverer of the electron) in 1926 scattered electrons from crystals and found diffraction patterns. These patterns are exactly consistent with interference of electrons having the de Broglie wavelength and are somewhat analogous to light interacting with a diffraction grating (Figure \(\PageIndex{1}\))
Connections: Waves
All microscopic particles, whether massless, like photons, or having mass, like electrons, have wave properties. The relationship between momentum and wavelength is fundamental for all particles.
De Broglie’s proposal of a wave nature for all particles initiated a remarkably productive era in which the foundations for quantum mechanics were laid. In 1926, the Austrian physicist Erwin Schrödinger (1887–1961) published four papers in which the wave nature of particles was treated explicitly with wave equations. At the same time, many others began important work. Among them was German physicist Werner Heisenberg (1901–1976) who, among many other contributions to quantum mechanics, formulated a mathematical treatment of the wave nature of matter that used matrices rather than wave equations. We will deal with some specifics in later sections, but it is worth noting that de Broglie’s work was a watershed for the development of quantum mechanics. De Broglie was awarded the Nobel Prize in 1929 for his vision, as were Davisson and G. P. Thomson in 1937 for their experimental verification of de Broglie’s hypothesis.
Example \(\PageIndex{1}\): Electron Wavelength versus Velocity and Energy
For an electron having a de Broglie wavelength of 0.167 nm (appropriate for interacting with crystal lattice structures that are about this size):
- Calculate the electron’s velocity, assuming it is nonrelativistic.
- Calculate the electron’s kinetic energy in eV.
Strategy
For part (a), since the de Broglie wavelength is given, the electron’s velocity can be obtained from \(\lambda = h/p\) by using the nonrelativistic formula for momentum, \(p = mv\). For part (b), once \(v\) is obtained (and it has been verified that \(v\) is nonrelativistic), the classical kinetic energy is simply \((1/2)mv^2\).
Solution for (a)
Substituting the nonrelativistic formula for momentum \((p = mv)\) into the de Broglie wavelength gives
\[\begin{align*} \lambda &= \dfrac{h}{p} \\[4pt] &= \dfrac{h}{mv}. \end{align*}\]
Solving for \(v\) gives
\[v =\dfrac{h}{m\lambda}.\nonumber\]
Substituting known values yields
\[\begin{align*} v &= \dfrac{6.63 \times 10^{-34} \, J \cdot s}{(9.11 \times 10^{-31} \, kg)(0.167 \times 10^{-9} \, m)} \\[4pt] &= 4.36 \times 10^6 \, m/s.\end{align*}\]
Solution for (b)
While fast compared with a car, this electron’s speed is not highly relativistic, and so we can comfortably use the classical formula to find the electron’s kinetic energy and convert it to eV as requested.
\[\begin{align*} KE &= \dfrac{1}{2} mv^2 \\[4pt] &= \dfrac{1}{2}(9.11 \times 10^{-31} \, kg)(4.36 \times 10^6 \times 10^6 \, m/s)^2 \\[4pt] &= (86.4 \times 10^{-18} \, J)\left(\dfrac{1 \, eV}{1.601 \times 10^{-19} \, J}\right) \\[4pt] &= 54.0 \, eV \end{align*} \]
Discussion
This low energy means that these 0.167-nm electrons could be obtained by accelerating them through a 54.0-V electrostatic potential, an easy task. The results also confirm the assumption that the electrons are nonrelativistic, since their velocity is just over 1% of the speed of light and the kinetic energy is about 0.01% of the rest energy of an electron (0.511 MeV). If the electrons had turned out to be relativistic, we would have had to use more involved calculations employing relativistic formulas.
Electron Microscopes
One consequence or use of the wave nature of matter is found in the electron microscope. As we have discussed, there is a limit to the detail observed with any probe having a wavelength. Resolution, or observable detail, is limited to about one wavelength. Since a potential of only 54 V can produce electrons with sub-nanometer wavelengths, it is easy to get electrons with much smaller wavelengths than those of visible light (hundreds of nanometers). Electron microscopes can, thus, be constructed to detect much smaller details than optical microscopes (Figure \(\PageIndex{2}\)).
There are basically two types of electron microscopes. The transmission electron microscope (TEM) accelerates electrons that are emitted from a hot filament (the cathode). The beam is broadened and then passes through the sample. A magnetic lens focuses the beam image onto a fluorescent screen, a photographic plate, or (most probably) a CCD (light sensitive camera), from which it is transferred to a computer. The TEM is similar to the optical microscope, but it requires a thin sample examined in a vacuum. However it can resolve details as small as 0.1 nm (\(10^{-10} \, m\)), providing magnifications of 100 million times the size of the original object. The TEM has allowed us to see individual atoms and structure of cell nuclei.
The scanning electron microscope (SEM) provides images by using secondary electrons produced by the primary beam interacting with the surface of the sample (Figure \(\PageIndex{2}\)). The SEM also uses magnetic lenses to focus the beam onto the sample. However, it moves the beam around electrically to “scan” the sample in the x and y directions. A CCD detector is used to process the data for each electron position, producing images like the one at the beginning of this chapter. The SEM has the advantage of not requiring a thin sample and of providing a 3-D view. However, its resolution is about ten times less than a TEM.
Electrons were the first particles with mass to be directly confirmed to have the wavelength proposed by de Broglie. Subsequently, protons, helium nuclei, neutrons, and many others have been observed to exhibit interference when they interact with objects having sizes similar to their de Broglie wavelength. The de Broglie wavelength for massless particles was well established in the 1920s for photons, and it has since been observed that all massless particles have a de Broglie wavelength \(\lambda = h/p\). The wave nature of all particles is a universal characteristic of nature. We shall see in following sections that implications of the de Broglie wavelength include the quantization of energy in atoms and molecules, and an alteration of our basic view of nature on the microscopic scale. The next section, for example, shows that there are limits to the precision with which we may make predictions, regardless of how hard we try. There are even limits to the precision with which we may measure an object’s location or energy.
MAKING CONNECTIONS
The wave nature of matter allows it to exhibit all the characteristics of other, more familiar, waves. Diffraction gratings, for example, produce diffraction patterns for light that depend on grating spacing and the wavelength of the light. This effect, as with most wave phenomena, is most pronounced when the wave interacts with objects having a size similar to its wavelength. For gratings, this is the spacing between multiple slits.) When electrons interact with a system having a spacing similar to the electron wavelength, they show the same types of interference patterns as light does for diffraction gratings, as shown at top left in Figure \(\PageIndex{3}\).
Atoms are spaced at regular intervals in a crystal as parallel planes, as shown in the bottom part of Figure \(\PageIndex{3}\). The spacings between these planes act like the openings in a diffraction grating. At certain incident angles, the paths of electrons scattering from successive planes differ by one wavelength and, thus, interfere constructively. At other angles, the path length differences are not an integral wavelength, and there is partial to total destructive interference. This type of scattering from a large crystal with well-defined lattice planes can produce dramatic interference patterns. It is called Bragg reflection , for the father-and-son team who first explored and analyzed it in some detail. The expanded view also shows the path-length differences and indicates how these depend on incident angle \(\theta\) in a manner similar to the diffraction patterns for x rays reflecting from a crystal.
Let us take the spacing between parallel planes of atoms in the crystal to be \(d\). As mentioned, if the path length difference (PLD) for the electrons is a whole number of wavelengths, there will be constructive interference —that is, \(PLD = n\lambda \, (n = 1, \, 2, \, 3, . . .)\). Because \(AB = BC = d \, \sin \, \theta\), we have constructive interference when
\[n\lambda = 2d \, \sin \, \theta.\]
This relationship is called the Bragg equation and applies not only to electrons but also to x rays.
The wavelength of matter is a submicroscopic characteristic that explains a macroscopic phenomenon such as Bragg reflection. Similarly, the wavelength of light is a submicroscopic characteristic that explains the macroscopic phenomenon of diffraction patterns.
Summary
- Particles of matter also have a wavelength, called the de Broglie wavelength, given by \(\lambda = \frac{h}{p}\), where \(p\) is momentum.
- Matter is found to have the same interference characteristics as any other wave.
Glossary
- de Broglie wavelength
- the wavelength possessed by a particle of matter, calculated by \(\lambda = h/p\)


3.5: Even More Direct Proofs- By Cases and By Exhaustion
Proof by exhaustion is the least attractive proof method from an aesthetic perspective. An exhaustive proof consists of literally (and exhaustively) checking every element of the universe to see if the given statement is true for it. Usually, of course, this is impossible because the universe of discourse is infinite; but when the universe of discourse is finite, one certainly can’t argue the validity of an exhaustive proof.
In the last few decades, the introduction of powerful computational assistance for mathematicians has lead to a funny situation. There is a growing list of important results that have been “proved” by exhaustion using a computer. Important examples of this phenomenon are the non-existence of a projective plane of order \(10\) [10] and the only known value of a Ramsey number for hypergraphs [13] .
Proof by cases is subtly different from exhaustive proof – for one thing a valid proof by cases can be used in an infinite universe. In a proof by cases, one has to divide the universe of discourse into a finite number of sets 1 and then provide a separate proof for each of the cases. A great many statements about the integers can be proved using the division of integers into even and odd. Another set of cases that is used frequently is the finite number of possible remainders obtained when dividing by an integer \(d\). (Note that even and odd correspond to the remainders \(0\) and \(1\) obtained after division by \(2\).)
A very famous instance of proof by cases is the computer-assisted proof of the four-color theorem. The four-color theorem is a result known to map makers for quite some time that says that \(4\) colors are always sufficient to color the nations on a map in such a way that countries sharing a boundary are always colored differently. Figure \(3.5.1\) shows one instance of an arrangement of nations that requires at least four different colors, the theorem says that four colors are always enough. It should be noted that real cartographers usually reserve a fifth color for oceans (and other water) and that it is possible to conceive of a map requiring five colors if one allows the nations to be non-contiguous. In \(1977\), Kenneth Appel and Wolfgang Haken proved the four-color theorem by reducing the infinitude of possibilities to \(1,936\) separate cases and analyzing each of these with a computer. The inelegance of a proof by cases is probably proportional to some power of the number of cases, but in any case, this proof is generally considered somewhat inelegant. Ever since the proof was announced there has been an ongoing effort to reduce the number of cases (currently the record is \(633\) cases – still far too many to be checked through without a computer) or to find a proof that does not rely on cases. For a good introductory article on the four-color theorem see [6] .
Most exhaustive proofs of statements that aren’t trivial tend to either be (literally) too exhausting or to seem rather contrived. One example of a situation in which an exhaustive proof of some statement exists is when the statement is thought to be universally true but no general proof is known – yet the statement has been checked for a large number of cases. Goldbach’s conjecture is one such statement. Christian Goldbach [4] was a mathematician born in Königsberg Prussia, who, curiously, did not make the conjecture 2 . which bears his name. In a letter to Leonard Euler, Goldbach conjectured that every odd number greater than \(5\) could be expressed as the sum of three primes (nowadays this is known as the weak Goldbach conjecture). Euler apparently liked the problem and replied to Goldbach stating what is now known as Goldbach’s conjecture: Every even number greater than \(2\) can be expressed as the sum of two primes. This statement has been lying around since \(1742\), and a great many of the world’s best mathematicians have made their attempts at proving it – to no avail! (Well, actually a lot of progress has been made but the result still hasn’t been proved.) It’s easy to verify the Goldbach conjecture for relatively small even numbers, so what has been done is/are proofs by exhaustion of Goldbach’s conjecture restricted to finite universes. As of this writing, the conjecture has been verified to be true of all even numbers less than \(2 × 10^{17}\).
Whenever an exhaustive proof, or a proof by cases exists for some statement it is generally felt that a direct proof would be more esthetically pleasing. If you are in a situation that doesn’t admit such a direct proof, you should at least seek a proof by cases using the minimum possible number of cases. For example, consider the following theorem and proof.
\(∀n ∈ \mathbb{Z} n^2\) is of the form \(4k\) or \(4k + 1\) for some \(k ∈ \mathbb{Z}\).
- Proof
-
We will consider the four cases determined by the four possible residues \(\text{mod } 4\).
case i) If \(n ≡ 0\) \((\text{mod } 4)\) then there is an integer \(m\) such that \(n = 4m\). It follows that \(n^2 = (4m)^2 = 16m^2\) is of the form \(4k\) where \(k\) is \(4m^2\).
case ii) If \(n ≡ 1\) \((\text{mod } 4)\) then there is an integer \(m\) such that \(n = 4m + 1\). It follows that \(n^2 = (4m + 1)^2 = 16m^2 + 8m + 1\) is of the form \(4k + 1\) where k is \(4m^2 + 2m\).
case iii) If \(n ≡ 2\) \((\text{mod } 4)\) then there is an integer \(m\) such that \(n = 4m + 2\). It follows that \(n^2 = (4m + 2)^2 = 16m^2 + 16m + 4\) is of the form \(4k\) where \(k\) is \(4m^2 + 4m + 1\).
case iv) If \(n ≡ 3\) \((\text{mod } 4)\) then there is an integer \(m\) such that \(n = 4m + 3\). It follows that \(n^2 = (4m + 3)^2 = 16m^2 + 24m + 9\) is of the form \(4k + 1\) where \(k\) is \(4m^2 + 6m + 2\).
Since these four cases exhaust the possibilities and since the desired result holds in each case, our proof is complete.
Q.E.D.
While the proof just stated is certainly valid, the argument is inelegant since a smaller number of cases would suffice.
The previous theorem can be proved using just two cases. Do so.
We’ll close this section by asking you to determine an exhaustive proof where the complexity of the argument is challenging but not too impossible.
Graph pebbling is an interesting concept originated by the famous combinatorialist Fan Chung. A “graph” (as the term is used here) is a collection of places or locations which are known as “nodes,” some of which are joined by paths or connections which are known as “edges.” Graphs have been studied by mathematicians for about \(400\) years, and many interesting problems can be put in this setting. Graph pebbling is a crude version of a broader problem in resource management – often a resource actually gets used in the process of transporting it. Think of the big tanker trucks that are used to transport gasoline. What do they run on? Well, actually they probably burn diesel — but the point is that in order to move the fuel around we have to consume some of it. Graph pebbling takes this to an extreme: in order to move one pebble we must consume one pebble.
Imagine that a bunch of pebbles are randomly distributed on the nodes of a graph, and that we are allowed to do graph pebbling moves – we remove two pebbles from some node and place a single pebble on a node that is connected to it. See Figure \(3.5.3\).
For any particular graph, we can ask for its pebbling number, \(ρ\). This is the smallest number so that if ρ pebbles are distributed in any way whatsoever on the nodes of the graph, it will be possible to use pebbling moves so as to get a pebble to any node.
For example, consider the triangle graph – three nodes which are all mutually connected. The pebbling number of this graph is \(3\). If we start with one pebble on each node we are already done; if there is a node that has two pebbles on it, we can use a pebbling move to reach either of the other two nodes.
There is a graph \(C_5\) which consists of \(5\) nodes connected in a circular fashion. Determine its pebbling number. Prove your answer exhaustively.
Hint: the pebbling number must be greater than \(4\) because if one pebble is placed on each of \(4\) nodes the configuration is unmovable (we need to have two pebbles on a node in order to be able to make a pebbling move at all) and so the \(5^{\text{th}}\) node can never be reached.
Exercises:
Prove that if \(n\) is an odd number then \(n^4 (\text{mod } 16) = 1\).
Prove that every prime number other than \(2\) and \(3\) has the form \(6q + 1\) or \(6q + 5\) for some integer \(q\).
- Hint
-
This problem involves thinking about cases as well as contrapositives.
Show that the sum of any three consecutive integers is divisible by \(3\).
There is a graph known as \(K_4\) that has \(4\) nodes and there is an edge between every pair of nodes. The pebbling number of \(K_4\) has to be at least \(4\) since it would be possible to put one pebble on each of \(3\) nodes and not be able to reach the remaining node using pebbling moves. Show that the pebbling number of \(K_4\) is actually \(4\).
Find the pebbling number of a graph whose nodes are the corners and whose edges are the, uhmm, edges of a cube.
A vampire number is a \(2n\) digit number \(v\) that factors as \(v = xy\) where \(x\) and \(y\) are \(n\) digit numbers and the digits of \(v\) are precisely the digits in \(x\) and \(y\) in some order. The numbers \(x\) and \(y\) are known as the “fangs” of \(v\). To eliminate trivial cases, both fangs can’t end with \(0\).
Show that there are no \(2\)-digit vampire numbers.
Show that there are seven \(4\)-digit vampire numbers
Lagrange’s theorem on representation of integers as sums of squares says that every positive integer can be expressed as the sum of at most \(4\) squares. For example, \(79 = 7^2 + 5^2 + 2^2 + 1^2\). Show (exhaustively) that \(15\) can not be represented using fewer than \(4\) squares.
Show that there are exactly \(15\) numbers \(x\) in the range \(1 ≤ x ≤ 100\) that can’t be represented using fewer than \(4\) squares.
The trichotomy property of the real numbers simply states that every real number is either positive or negative or zero. Trichotomy can be used to prove many statements by looking at the three cases that it guarantees. Develop a proof (by cases) that the square of any real number is non-negative.
Consider the game called “binary determinant tic-tac-toe” 3 which is played by two players who alternately fill in the entries of a \(3 × 3\) array. Player One goes first, placing \(1\)’s in the array and player Zero goes second, placing \(0\)’s. Player One’s goal is that the final array have determinant \(1\), and player Zero’s goal is that the determinant be \(0\). The determinant calculations are carried out \(\text{mod } 2\).
Show that player Zero can always win a game of binary determinant tic-tac-toe by the method of exhaustion.
Notes
2. This conjecture was discussed previously in the exercises of Section 1.2
3. This question was problem A4 in the 63rd annual William Lowell Putnam Mathematics Competition (2002). There are three collections of questions and answers from previous Putnam exams available from the MAA [1 , 7 , 9]


15.3: Population Growth and Regulation
By the end of this section, you will be able to do the following:
- Explain the characteristics of and differences between exponential and logistic growth patterns
- Give examples of exponential and logistic growth in natural populations
- Give examples of how the carrying capacity of a habitat may change
- Compare and contrast density-dependent growth regulation and density-independent growth regulation giving examples
Population ecologists make use of a variety of methods to model population dynamics. An accurate model should be able to describe the changes occurring in a population and predict future changes.
Population Growth
The two simplest models of population growth use deterministic equations (equations that do not account for random events) to describe the rate of change in the size of a population over time. The first of these models, exponential growth, describes theoretical populations that increase in numbers without any limits to their growth. The second model, logistic growth, introduces limits to reproductive growth that become more intense as the population size increases. Neither model adequately describes natural populations, but they provide points of comparison.
Exponential Growth
Charles Darwin, in developing his theory of natural selection, was influenced by the English clergyman Thomas Malthus. Malthus published his book in 1798 stating that populations with abundant natural resources grow very rapidly; however, they limit further growth by depleting their resources. The early pattern of accelerating population size is called exponential growth.
The best example of exponential growth in organisms is seen in bacteria. Bacteria are prokaryotes that reproduce largely by binary fission. This division takes about an hour for many bacterial species. If 1000 bacteria are placed in a large flask with an abundant supply of nutrients (so the nutrients will not become quickly depleted), the number of bacteria will have doubled from 1000 to 2000 after just an hour. In another hour, each of the 2000 bacteria will divide, producing 4000 bacteria. After the third hour, there should be 8000 bacteria in the flask. The important concept of exponential growth is that the growth rate—the number of organisms added in each reproductive generation—is itself increasing; that is, the population size is increasing at a greater and greater rate. After 24 of these cycles, the population would have increased from 1000 to more than 16 billion bacteria. When the population size, N , is plotted over time, a J-shaped growth curve is produced (Figure \(\PageIndex{1}\) a ).
The bacteria-in-a-flask example is not truly representative of the real world where resources are usually limited. However, when a species is introduced into a new habitat that it finds suitable, it may show exponential growth for a while. In the case of the bacteria in the flask, some bacteria will die during the experiment and thus not reproduce; therefore, the growth rate is lowered from a maximal rate in which there is no mortality. The growth rate of a population is largely determined by subtracting the death rate, D , (number organisms that die during an interval) from the birth rate, B , (number organisms that are born during an interval). The growth rate can be expressed in a simple equation that combines the birth and death rates into a single factor: r . This is shown in the following formula:
\[\text{Population growth} = rN \nonumber\]
The value of r can be positive, meaning the population is increasing in size (the rate of change is positive); or negative, meaning the population is decreasing in size; or zero, in which case the population size is unchanging, a condition known as zero population growth.
Logistic Growth
Extended exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. Charles Darwin recognized this fact in his description of the “struggle for existence,” which states that individuals will compete (with members of their own or other species) for limited resources. The successful ones are more likely to survive and pass on the traits that made them successful to the next generation at a greater rate (natural selection). To model the reality of limited resources, population ecologists developed the logistic growth model.
Carrying Capacity and the Logistic Model
In the real world, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where there are few individuals and plentiful resources, but when the number of individuals gets large enough, resources will be depleted and the growth rate will slow down. Eventually, the growth rate will plateau or level off (Figure \(\PageIndex{1}\) b ). This population size, which is determined by the maximum population size that a particular environment can sustain, is called the carrying capacity, or K . In real populations, a growing population often overshoots its carrying capacity, and the death rate increases beyond the birth rate causing the population size to decline back to the carrying capacity or below it. Most populations usually fluctuate around the carrying capacity in an undulating fashion rather than existing right at it.
The formula used to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. The expression “ K – N ” is equal to the number of individuals that may be added to a population at a given time, and “ K – N ” divided by “ K ” is the fraction of the carrying capacity available for further growth. Thus, the exponential growth model is restricted by this factor to generate the logistic growth equation:
\[\text{Population growth} = rN \left[\dfrac{K-N}{K}\right] \nonumber\]
Notice that when N is almost zero the quantity in brackets is almost equal to 1 (or K / K ) and growth is close to exponential. When the population size is equal to the carrying capacity, or N = K , the quantity in brackets is equal to zero and growth is equal to zero. A graph of this equation (logistic growth) yields the S-shaped curve (Figure \(\PageIndex{1}\) b ). It is a more realistic model of population growth than exponential growth. There are three different sections to an S-shaped curve. Initially, growth is exponential because there are few individuals and ample resources available. Then, as resources begin to become limited, the growth rate decreases. Finally, the growth rate levels off at the carrying capacity of the environment, with little change in population number over time.
Role of Intraspecific Competition
The logistic model assumes that every individual within a population will have equal access to resources and, thus, an equal chance for survival. For plants, the amount of water, sunlight, nutrients, and space to grow are the important resources, whereas in animals, important resources include food, water, shelter, nesting space, and mates.
In the real world, phenotypic variation among individuals within a population means that some individuals will be better adapted to their environment than others. The resulting competition for resources among population members of the same species is termed intraspecific competition. Intraspecific competition may not affect populations that are well below their carrying capacity, as resources are plentiful and all individuals can obtain what they need. However, as population size increases, this competition intensifies. In addition, the accumulation of waste products can reduce carrying capacity in an environment.
Examples of Logistic Growth
Yeast, a microscopic fungus used to make bread and alcoholic beverages, exhibits the classical S-shaped curve when grown in a test tube (Figure \(\PageIndex{2}\) a ). Its growth levels off as the population depletes the nutrients that are necessary for its growth. In the real world, however, there are variations to this idealized curve. Examples in wild populations include sheep and harbor seals (Figure \(\PageIndex{2}\) b ). In both examples, the population size exceeds the carrying capacity for short periods of time and then falls below the carrying capacity afterwards. This fluctuation in population size continues to occur as the population oscillates around its carrying capacity. Still, even with this oscillation, the logistic model is confirmed.
ART CONNECTION
If the major food source of seals declines due to pollution or overfishing, which of the following would likely occur?
- The carrying capacity of seals would decrease, as would the seal population.
- The carrying capacity of seals would decrease, but the seal population would remain the same.
- The number of seal deaths would increase, but the number of births would also increase, so the population size would remain the same.
- The carrying capacity of seals would remain the same, but the population of seals would decrease.
Population Dynamics and Regulation
The logistic model of population growth, while valid in many natural populations and a useful model, is a simplification of real-world population dynamics. Implicit in the model is that the carrying capacity of the environment does not change, which is not the case. The carrying capacity varies annually. For example, some summers are hot and dry whereas others are cold and wet; in many areas, the carrying capacity during the winter is much lower than it is during the summer. Also, natural events such as earthquakes, volcanoes, and fires can alter an environment and hence its carrying capacity. Additionally, populations do not usually exist in isolation. They share the environment with other species, competing with them for the same resources (interspecific competition). These factors are also important to understanding how a specific population will grow.
Population growth is regulated in a variety of ways. These are grouped into density-dependent factors, in which the density of the population affects growth rate and mortality, and density-independent factors, which cause mortality in a population regardless of population density. Wildlife biologists, in particular, want to understand both types because this helps them manage populations and prevent extinction or overpopulation.
Density-dependent Regulation
Most density-dependent factors are biological in nature and include predation, inter- and intraspecific competition, and parasites. Usually, the denser a population is, the greater its mortality rate. For example, during intra- and interspecific competition, the reproductive rates of the species will usually be lower, reducing their populations’ rate of growth. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its food source. Also, when the population is denser, diseases spread more rapidly among the members of the population, which affect the mortality rate.
Density dependent regulation was studied in a natural experiment with wild donkey populations on two sites in Australia. 1 On one site the population was reduced by a population control program; the population on the other site received no interference. The high-density plot was twice as dense as the low-density plot. From 1986 to 1987 the high-density plot saw no change in donkey density, while the low-density plot saw an increase in donkey density. The difference in the growth rates of the two populations was caused by mortality, not by a difference in birth rates. The researchers found that numbers of offspring birthed by each mother was unaffected by density. Growth rates in the two populations were different mostly because of juvenile mortality caused by the mother’s malnutrition due to scarce high-quality food in the dense population. Figure \(\PageIndex{3}\) shows the difference in age-specific mortalities in the two populations.
Density-independent Regulation and Interaction with Density-dependent Factors
Many factors that are typically physical in nature cause mortality of a population regardless of its density. These factors include weather, natural disasters, and pollution.  Its chances of survival are the same whether the population density is high or low. The same holds true for cold winter weather.
In real-life situations, population regulation is very complicated and density-dependent and independent factors can interact. A dense population that suffers mortality from a density-independent cause will be able to recover differently than a sparse population. For example, a population of deer affected by a harsh winter will recover faster if there are more deer remaining to reproduce.
EVOLUTION IN ACTION: Why Did the Woolly Mammoth Go Extinct?
Woolly mammoths began to go extinct about 10,000 years ago, soon after paleontologists believe humans able to hunt them began to colonize North America and northern Eurasia (Figure \(\PageIndex{4}\)). A mammoth population survived on Wrangel Island, in the East Siberian Sea, and was isolated from human contact until as recently as 1700 BC. We know a lot about these animals from carcasses found frozen in the ice of Siberia and other northern regions.
It is commonly thought that climate change and human hunting led to their extinction.  A 2012 study concluded that no single factor was exclusively responsible for the extinction of these magnificent creatures. 3 In addition to climate change and reduction of habitat, scientists demonstrated another important factor in the mammoth’s extinction was the migration of human hunters across the Bering Strait to North America during the last ice age 20,000 years ago.
The maintenance of stable populations was and is very complex, with many interacting factors determining the outcome. It is important to remember that humans are also part of nature. Once we contributed to a species’ decline using primitive hunting technology only.
Demographic-Based Population Models
Population ecologists have hypothesized that suites of characteristics may evolve in species that lead to particular adaptations to their environments. These adaptations impact the kind of population growth their species experience. Life history characteristics such as birth rates, age at first reproduction, the numbers of offspring, and even death rates evolve just like anatomy or behavior, leading to adaptations that affect population growth. Population ecologists have described a continuum of life-history “strategies” with K -selected species on one end and r -selected species on the other. K -selected species are adapted to stable, predictable environments. Populations of K -selected species tend to exist close to their carrying capacity. These species tend to have larger, but fewer, offspring and contribute large amounts of resources to each offspring. Elephants would be an example of a K -selected species. r -selected species are adapted to unstable and unpredictable environments. They have large numbers of small offspring. Animals that are r -selected do not provide a lot of resources or parental care to offspring, and the offspring are relatively self-sufficient at birth. Examples of r -selected species are marine invertebrates such as jellyfish and plants such as the dandelion. The two extreme strategies are at two ends of a continuum on which real species life histories will exist. In addition, life history strategies do not need to evolve as suites, but can evolve independently of each other, so each species may have some characteristics that trend toward one extreme or the other.
Art Exercise
Figure \(\PageIndex{2}\): If the major food source of seals declines due to pollution or overfishing, which of the following would likely occur?
- The carrying capacity of seals would decrease, as would the seal population.
- The carrying capacity of seals would decrease, but the seal population would remain the same.
- The number of seal deaths would increase, but the number of births would also increase, so the population size would remain the same.
- The carrying capacity of seals would remain the same, but the population of seals would decrease.
- Answer
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A: The carrying capacity of seals would decrease, as would the seal population.
Footnotes
- 1 David Choquenot, “Density-Dependent Growth, Body Condition, and Demography in Feral Donkeys: Testing the Food Hypothesis,” Ecology 72, no. 3 (June 1991):805–813.
- 2 David Nogués-Bravo et al., “Climate Change, Humans, and the Extinction of the Woolly Mammoth.” PLoS Biol 6 (April 2008): e79, doi:10.1371/journal.pbio.0060079.
- 3 G.M. MacDonald et al., “Pattern of Extinction of the Woolly Mammoth in Beringia.” Nature Communications 3, no. 893 (June 2012), doi:10.1038/ncomms1881.
Contributors and Attributions
Remixed and/or curated from the following works:
Fowler, S., Roush, R., & Wise, J. (2013). 19.2 Population Growth and Regulation . In Concepts of Biology . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/concepts-biology/pages/1-introduction ).


9.3: MacConkey Media, MAC
- Discuss the purpose of MAC media for selective and differential colony growth.
- Inoculate MAC agar plates using aseptic technique.
- Determine rates of lactose fermentation in gram negative bacteria.
MacConkey Media
Mac Conkey Media, or MAC , is a differential and selective agar used to isolate bacteria in the Enterobacteriaceae family.
The Enterobacteriaceae family includes " enteric " or intestinal bacteria typically found in the human intestines. These bacterias are gram-negative facultative anaerobes who have adapted to the presence of intestinal bile salts and are capable of migrating to the urinary tract to cause infections. Enterobacteriaceae also have different rates of lactose fermentation, making the bacteria either a coliform or non-coliform class. Coliform bacteria, like E. coli, can rapidly and completely ferment lactose. This rapid fermentation produces acid as a by-product, which can alter the coliform's colony morphology and surrounding environment. Non-coliform bacteria either slowly and incompletely ferment lactose or they are unable to ferment lactose at all. Non-coliform bacteria, like Yersinia pestis, are more likely to produce very low, negligible levels of acid or none at all. Differences in lactose fermentation of Enterobacteriaceae contribute to colony morphology and media appearance when using MAC agar plates.
Figure 1. Examples of coliform and non-coliform bacteria.
MAC is a selective media as it has the ability to inhibit gram positive growth. MAC media is made with crystal violet dye and bile salts which are capable of inhibiting most gram-positive bacterial growth. Gram-negative enteric bacteria are not affected as these species normally grow in the presence of bile salts in the human gut.
MAC is a differential media based on the ability of the bacteria to ferment lactose present in the agar. MAC media is also made using a pH indicator called Neutral Red, and this indicator can change the color of the bacterial colonies based on their fermentation rate. Rapid lactose fermenters, enteric coliforms, will produce high levels of acid during lactose fermentation. High acid production will lower the pH of the MAC media and, once the pH drops below 6.8, the neutral red indicator will activate and turn the media a bright red/pink color. The Neutral Red will also be absorbed by the bacteria, changing colony color to the same bright red/pink color of the media. Bacteria that can not ferment lactose, non-coliforms, must use other nutrients for energy production. Instead of lactose, non-coliform bacteria can use nitrogen sources like peptone. Peptone fermentation will produce ammonia as a by-product instead of acid. Ammonia will raise the pH of the MAC agar, Neutral Red will not activated, and bacterial colonies will be white or colorless. Under these conditions, the MAC agar will also turn yellow in color.
Figure 2. Gram negative bacteria that can grow on MAC agar will have different colony colors depending on their ability to ferment lactose. Rapid lactose fermenters will produce high quantities of acid, turning the media red. Bacteria that can not ferment lactose will be forced to find other energy sources and will not produce acid. These colonies will remain colorless and the agar may turn yellow in color.
Pseudomonas aeruginosa
The genus Pseudomonas contains a diverse group of gram-negative rod-shaped bacteria. Many Pseudomonas species are pathogenic for humans including Pseudomonas aeruginosa. P. aeruginosa is an opportunistic pathogen that targets patients with cystic fibrosis and can cause urinary tract infections (UTIs). (Openstax, 2024) The CDC estimates that P. aeruginosa causes approximately 30,000 infections and 2,700 deaths annually. (CDC, 2024) P. aeruginosa infections are difficult to treat as the bacteria is highly resistant to antibiotics. One diagnostic tool to determine if an infection is caused by P. aeruginosa is MacConkey Agar.
MacConkey agar is made with the sugar lactose and pH indicator Neutral Red. This agar will promote the growth of gram-negative species like P. aeruginosa while differentiating species based on lactose fermentation and pH. Patients suffering from a UTI suspected to be caused by P. aeruginosa will first need submit a clean urine sample. The patient must first wash their urethral opening prior to providing the urine sample to prevent contamination by their normal microbiota. The uncontaminated urine sample will then be grown on MacConkey agar.
P. aeruginosa can not ferment lactose. This means the bacteria will not alter the color of the agar plate. Thus, if a patients urine sample on MacConkey comes back positive for growth but has no change to the color of the media, the UTI is likely the result of a P. aeruginosa infection. P. aeruginosa cells may produce a blue-green pigment called pyocyanin in response to environmental stress when grown on MacConkey, further helping identify the microbe.
Figure 3. Pseudomonas aeruginosa can grow on MAC as it is a gram-negative bacterium. The bacteria can not ferment lactose,and will not alter the color of the media (black arrows). P. aeruginosa may become stressed from growth on MAC, however, and start to produce a blue-green pigment called pyocyanin (white arrows). Pyocyanin helps the bacteria consume more iron in low-iron environments like MAC agar.
Attributions
"Microbiology Labs II: Results, 12.6.1 MacConkey Agar" by Dr. Gary Kaiser , LibreTexts: Biology , Community College of Baltimore County, Catonsville Campus is licensed under CC BY 4.0
"Microbiology Labs II: Pure Cultures, 3.4 Use of Specialized Media" by Dr. Gary Kaiser , LibreTexts: Biology , Community College of Baltimore County, Catonsville Campus is licensed under CC BY 4.0
"Bio 221 Lab: Physiological Tests, 22.2 Selective and Differential Media-MacConkey, EMB, MSA" by Kelly Burke , LibreTexts: Biology , College of The Canyons is licensed under CC BY
"Microbiology Textbook: Chapter 9, Microbial Growth" by Openstax , Digital ISBN 13: 978-1-947172-23-4 is licensed under CC BY 4.0
"Microbiology Textbook: Chapter 4, Prokaryotic Diversity" by Openstax , Digital ISBN 13: 978-1-947172-23-4 is licensed under CC BY 4.0
"About Pseudomonas aeruginosa" by Centers for Diseases Control and Prevention , Use of CDC Materials Statement is in the Public Domain
"Microbiology Textbook: Chapter 12, Modern Applications of Microbial Genetics" by Openstax , Digital ISBN: 13: 978-1-947172-23-4 is licensed under CC BY 4.0
"Microbiology Textbook: Chapter 21, Skin and Eye Infections" by Openstax , Digital ISBN: 13: 978-1-947172-23-4 is licensed under CC BY 4.0
Image Citations
Figure 1, Modified From:
- "E. coli Bacteria<PHONE_NUMBER>).jpg" by National Institute of Allergy and Infectious Diseases , Wikimedia Commons is in the Public Domain
- "Yersinia pestis scanned with electron micrograph.jpg" by National Institute of Allergy and Infectious Diseases , Wikimedia Commons is in the Public Domain
Figure 2, Modified From:
- "MacConkey agar with LF and LF colonies.jpg" by Medimicro, Wikimedia Commons is in the Public Domain
Figure 3, Modified From:
- "Microbiology Labs II: Results, 12.6.1 MacConkey Agar" by Dr. Gary Kaiser , LibreTexts: Biology , Community College of Baltimore County, Catonsville Campus is licensed under CC BY 4.0


2.7A: Structure, Type, and Location of Cartilage
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Cartilage is an avascular, flexible connective tissue located throughout the body that provides support and cushioning for adjacent tissues.
LEARNING OBJECTIVE
Differentiate among the types of cartilage
Key Takeaways
Key Points
- Cartilage is a flexible connective tissue that differs from bone in several ways; it is avascular and its microarchitecture is less organized than bone.
- Cartilage is not innervated and therefore relies on diffusion to obtain nutrients. This causes it to heal very slowly.
- The main cell types in cartilage are chondrocytes, the ground substance is chondroitin sulfate, and the fibrous sheath is called perichondrium.
- There are three types of cartilage: hyaline, fibrous, and elastic cartilage.
- Hyaline cartilage is the most widespread type and resembles glass. In the embryo, bone begins as hyaline cartilage and later ossifies.
- Fibrous cartilage has many collagen fibers and is found in the intervertebral discs and pubic symphysis.
- Elastic cartilage is springy, yellow, and elastic and is found in the internal support of the external ear and in the epiglottis.
Key Terms
chondroitin sulfate : An important structural component of cartilage that provides much of its resistance to compression.
connective tissue : A type of tissue found in animals whose main function is to bind other tissue systems (such as muscle to skin) or organs. It consists of the following three elements: cells, fibers, and a ground substance (or extracellular matrix).
hyaline cartilage : A type of cartilage found on many joint surfaces; it contains no nerves or blood vessels, and its structure is relatively simple.
temporal mandibular joint : A joint of the jaw that connects it to the temporal bones of the skull.
Chondrocytes : Cells that form and maintain the cartilage.
What is Cartilage?
Cartilage is a flexible connective tissue that differs from bone in several ways. For one, the primary cell types are chondrocytes as opposed to osteocytes. Chondrocytes are first chondroblast cells that produce the collagen extracellular matrix (ECM) and then get caught in the matrix. They lie in spaces called lacunae with up to eight chondrocytes located in each.
Chondrocytes rely on diffusion to obtain nutrients as, unlike bone, cartilage is avascular, meaning there are no vessels to carry blood to cartilage tissue. This lack of blood supply causes cartilage to heal very slowly compared with bone.
The base substance of cartilage is chondroitin sulfate, and the microarchitecture is substantially less organized than in bone. The cartilage fibrous sheath is called the perichondrium. The division of cells within cartilage occurs very slowly, and thus growth in cartilage is usually not based on an increase in size or mass of the cartilage itself.
Articular cartilage function is dependent on the molecular composition of its ECM, which consists mainly of proteoglycans and collagens. The remodeling of cartilage is predominantly affected by changes and rearrangements of the collagen matrix, which responds to tensile and compressive forces experienced by the cartilage.
Cartilage types: Images of microscopic views of the different types of cartilage: elastic, hyaline, and fibrous. Elastic cartilage has the most ECM; hyaline a middle amount; and fibrous cartilage has the least amount of ECM.
Types of Cartilage
There are three major types of cartilage: hyaline cartilage, fibrocartilage, and elastic cartilage.
Hyaline Cartilage
Hyaline cartilage is the most widespread cartilage type and, in adults, it forms the articular surfaces of long bones, the rib tips, the rings of the trachea, and parts of the skull. This type of cartilage is predominately collagen (yet with few collagen fibers), and its name refers to its glassy appearance.
In the embryo, bones form first as hyaline cartilage before ossifying as development progresses. Hyaline cartilage is covered externally by a fibrous membrane, called the perichondrium, except at the articular ends of bones; it also occurs under the skin (for instance, ears and nose).
Hyaline cartilage is found on many joint surfaces. It contains no nerves or blood vessels, and its structure is relatively simple.
If a thin slice of cartilage is examined under the microscope, it will be found to consist of cells of a rounded or bluntly angular form, lying in groups of two or more in a granular or almost homogeneous matrix. These cells have generally straight outlines where they are in contact with each other, with the rest of their circumference rounded.
They consist of translucent protoplasm in which fine interlacing filaments and minute granules are sometimes present. Embedded in this are one or two round nuclei with the usual intranuclear network.
Fibrocartilage
Fibrous cartilage has lots of collagen fibers (Type I and Type II), and it tends to grade into dense tendon and ligament tissue. White fibrocartilage consists of a mixture of white fibrous tissue and cartilaginous tissue in various proportions.
It owes its flexibility and toughness to the fibrous tissue, and its elasticity to the cartilaginous tissue. It is the only type of cartilage that contains type I collagen in addition to the normal type II.
Fibrocartilage is found in the pubic symphysis, the annulus fibrosus of intervertebral discs, menisci, and the temporal mandibular joint.
Elastic Cartilage
Elastic or yellow cartilage contains elastic fiber networks and collagen fibers. The principal protein is elastin.
Elastic cartilage is histologically similar to hyaline cartilage but contains many yellow elastic fibers lying in a solid matrix. These fibers form bundles that appear dark under a microscope. They give elastic cartilage great flexibility so it can withstand repeated bending.
Chondrocytes lie between the fibers. Elastic cartilage is found in the epiglottis (part of the larynx) and the pinnae (the external ear flaps of many mammals, including humans).


2: Equations and Inequalities
Source: Boundless. “Equations and Inequalities.” Boundless Algebra . Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/
Source: Boundless. “Equations and Inequalities.” Boundless Algebra . Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/
An equation states that two expressions are equal, while an inequality relates two different values.
Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/
Source: Boundless. “Equations and Inequalities.” Boundless Algebra. Boundless, 21 Jul. 2015. Retrieved 22 Dec. 2015 from www.boundless.com/algebra/te...ties-63-10904/
Recall that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.
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- 2.1: The Rectangular Coordinate Systems and Graphs
- Descartes introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Descartes named the horizontal axis the \(x\)-axis and the vertical axis the \(y\)-axis. This system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the \(x\)-axis and the \(y\)-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant.
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- 2.3: Models and Applications
- A linear equation can be used to solve for an unknown in a number problem. Applications can be written as mathematical problems by identifying known quantities and assigning a variable to unknown quantities. There are many known formulas that can be used to solve applications. Distance problems are solved using the \(d = rt\) formula. Many geometry problems are solved using the perimeter formula \(P =2L+2W\), the area formula \(A =LW\), or the volume formula \(V =LWH\).
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- 2.4: Complex Numbers
- The square root of any negative number can be written as a multiple of i. To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis. Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts. Complex numbers can be multiplied and divided.
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- 2.5: Quadratic Equations
- Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
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- 2.6: Other Types of Equations
- Rational exponents can be rewritten several ways depending on what is most convenient for the problem. To solve, both sides of the equation are raised to a power that will render the exponent on the variable equal to 1. Factoring extends to higher-order polynomials when it involves factoring out the GCF or factoring by grouping. We can solve radical equations by isolating the radical and raising both sides of the equation to a power that matches the index.
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- 2.8: Circles
- A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose endpoints are on the circle. In addition, a circle can be formed by the intersection of a cone and a plane that is perpendicular to the axis of the cone.
Contributors and Attributions
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Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus .


<IP_ADDRESS>: Pathogen-Associated Molecular Patterns (PAMPs) and Danger-Associated Molecular Patterns (DAMPs)
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State how long it takes for early induced innate immunity to become activated and what it involves.
State what is meant by pathogen-associated molecular patterns (PAMPs), and the role PAMPs play in inducing innate immunity.
Name at least 5 PAMPS associated with bacteria.
Name at least 2 PAMPS associated with viruses.
Define DAMPs and give two examples.
Examples of microbial-associated PAMPs include:
- lipopolysaccharide (LPS) from the outer membrane of the Gram-negative cell wall (see Figure \(\PageIndex{1}\)A);
- bacterial lipoproteins and lipopeptides (see Figure \(\PageIndex{1}\)A);
- porins in the outer membrane of the Gram-negative cell wall (see Figure \(\PageIndex{1}\)A);
- peptidoglycan found abundantly in the Gram-positive cell wall and to a lesser degree in the gram-negative cell wall (see Figure \(\PageIndex{1}\)B);
- lipoteichoic acids found in the Gram-positive cell wall (Figure \(\PageIndex{1}\)B);
- lipoarabinomannan and mycolic acids found in acid-fast cell walls (Figure \(\PageIndex{2}\)B)
- mannose-rich glycans (short carbohydrate chains with the sugar mannose or fructose as the terminal sugar). These are common in microbial glycoproteins and glycolipids but rare in those of humans (see Figure \(\PageIndex{6}\)) .
- flagellin found in bacterial flagella;
- bacterial and viral nucleic acid. Bacterial and viral genomes contain a high frequency of unmethylated cytosine-guanine dinucleotide or CpG sequences (a cytosine lacking a methyl or CH 3 group and located adjacent to a guanine). Mammalian DNA has a low frequency of CpG sequences and most are methylated which may mask recognition by pattern-recognition receptors . Also, human DNA and RNA does not normally enter cellular endosomes where the pattern-recognition receptors for microbial DNA and RNA are located;
- N -formylmethionine , an amino acid common to bacterial proteins;
- double-stranded viral RNA unique to many viruses in some stage of their replication;
- single-stranded viral RNA from many` viruses having an RNA genome;
- lipoteichoic acids, glycolipids, and zymosan from yeast cell walls; and
- phosphorylcholine and other lipids common to microbial membranes.
Examples of DAMPs associated with stressed, injured, infected, or transformed host cells and not found on normal cells include:
- heat-shock proteins;
- altered membrane phospholipids; and
- molecules normally located inside phagosomes and lysosomes that enter the cytosol only when these membrane-bound compartments are damaged as a result of infection, including antibodies bound to microbes from opsonization.
- molecules normally found within cells, such as ATP, DNA, and RNA, that spill out of damaged cells.
To recognize PAMPs such as those listed above, various body cells have a variety of corresponding receptors called pattern-recognition receptors or PRRs capable of binding specifically to conserved portions of these molecules. Cells that typically have pattern recognition receptors include macrophages , dendritic cells , endothelial cells , mucosal epithelial cells, and lymphocytes .
What are DAMPs and why would it be an advantage for them to initiate an inflammatory response similar to PAMPs?
Summary
- Early induced innate immunity begins 4 - 96 hours after exposure to an infectious agent and involves the recruitment of defense cells as a result of pathogen-associated molecular patterns or PAMPS binding to pattern-recognition receptors or PRRs.
- Pathogen-associated molecular patterns or PAMPs are molecules shared by groups of related microbes that are essential for the survival of those organisms and are not found associated with mammalian cells. Examples include LPS, porins, peptidoglycan, lipoteichoic acids, mannose-rich glycans, flagellin, bacterial and viral genomes, mycolic acid, and lipoarabinomannan.
- Danger-associated molecular patterns or DAMPs are unique molecules displayed on stressed, injured, infected, or transformed human cells also be recognized as a part of innate immunity. Examples include heat-shock proteins and altered membrane phospholipids.
- PAMPs and DAMPs bind to pattern-recognition receptors or PRRs associated with body cells to induce innate immunity.


3.3: Marriage and Relationships
What is a “healthy marriage?
There are at least two characteristics that all healthy marriages have in common.
- First, they are mutually enriching, and
- Second, both spouses have a deep respect for each other.
It is a mutually satisfying relationship that is beneficial to the husband, wife and children (if present). It is a relationship that is committed to ongoing growth, the use of effective communication skills and the use of successful conflict management skills.
Healthy Marriage Matters
Research suggests that children who grow up in healthy married, two-parent families do better on a host of outcomes than those who do not. Further, many social problems affecting children, families, and communities could be prevented if more children grew up in healthy, married families.
Examples of social science findings include:
- Married couples seem to build more wealth, on average, than singles or cohabiting couples, thus decreasing the likelihood that their children will grow up in poverty.
- Children who live in a two-parent, married household enjoy better physical health, on average, than children in non-married households.
- Healthy marriages reduce the risk of adults and children either perpetrating, or being victimized by, crime.Benefits of Healthy Marriages
For Children and Youth
Researchers have found many benefits for children and youth who are raised by parents in healthy marriages, compared to unhealthy marriages, including the following:
- More likely to attend college
- Demonstrate less behavioral problems in school
- Less likely to be a victim of physical or sexual abuse
- Less likely to abuse drugs or alcohol
- Less likely to commit delinquent behaviors
- More likely to succeed academically
- Physically healthier
- Emotionally healthier
- Less likely to attempt or commit suicide
- Decreases their chances of divorcing when they get married
- Less likely to become pregnant as a teenager, or impregnate someone.
- Less likely to be sexually active as teenagers
- Less likely to contract STD’s
- Less likely to be raised in poverty
For Women
Researchers have found many benefits for women who are in healthy marriages, compared to unhealthy marriages, including the following:
- More satisfying relationship
- Emotionally healthier
- Wealthier
- Less likely to be victims of domestic violence, sexual assault, or other violent crimes
- Less likely to attempt or commit suicide
- Decrease risk of drug and alcohol abuse
- Less likely to contract STD’s
- Less likely to remain or end up in poverty
- Have better relationships with their children
- Physically healthier
For Men
Researchers have found many benefits for men who are in healthy marriages, compared to unhealthy marriages, including the following:
- Physically healthier
- Wealthier
- Increase in the stability of employment
- Higher wages
- Emotionally healthier
- Decrease risk of drug and alcohol abuse
- Have better relationships with their children
- Less likely to commit violent crimes
- Less likely to contract STD’s
- Less likely to attempt or commit suicide
For Communities
Researchers have found many benefits for communities when they have a higher percentage of couples in healthy marriages, compared to unhealthy marriages, including the following:
- Higher rates of physically healthy citizens
- Higher rates of emotionally healthy citizens
- Higher rates of educated citizens
- Lower domestic violence rates
- Lower crime statistics
- Lower teen age pregnancy rates
- Lower rates of juvenile delinquency
- Higher rates of home ownership
- Lower rates of migration
- Higher property values
- Decreased need for social services
Marital Status and Health: United States, 1999–2002
A report from the Centers for Disease Control and Prevention suggests that married adults are healthier than divorced, widowed or never married adults.
The report, “Marital Status and Health: United States, 1999-2002,” was based on interviews with 127,545 adults aged 18 and over as part of the National Health Interview Survey, conducted by CDC’s National Center for Health Statistics. The study looked at health status and limitations, health conditions, health related behaviors according to marital status and also by age, race/ethnicity and socioeconomic factors such as education and poverty status.
Among the findings in the report:
- Nearly 60% of adults are married, 10.4% are separated or divorced, 6.6% are widowed, 19% are never married and 5.7% are living with a partner. Marital status varies greatly among race/ethnic groups: approximately 61 percent of white adults, 58 percent of Hispanic adults, and 38 percent of black adults are married, according to the survey.
- Married adults are less likely than other adults to be in fair or poor health, and are less likely to suffer from health conditions such as headaches and serious psychological distress.
- Married adults are less likely be limited in various activities, including work and other activities of daily living.
- Married adults are less likely to smoke, drink heavily or be physically inactive. However, married men are more likely to be overweight or obese than other men.
- Adults who live in cohabiting relationships are more likely to have health problems than married adults and more closely resemble divorced and separated adults.
- The association between marital status and health is most striking in the youngest age group although it persists throughout the age groups studied.
While the results show that married adults are generally in better health than unmarried adults, the reasons for better health status among married adults cannot be determined with cross-sectional data collected in the National Health Interview Survey.
The Effects of Marriage on Health
Understanding the Marriage-Health Connection
The relationship between marriage and health is complex. Marital status can both affect health outcomes and be affected by them. Healthier people may have a better chance of marrying and staying married because they may be viewed as more desirable marriage partners based on their physical attractiveness, earnings potential, mental well-being, degree of self-sufficiency, or likely longevity. Social scientists describe this pattern as the selection of healthy people into marriage. If this is the only reason for the correlation between marriage and health, then marriage is not causing better health. Instead, the observed health differences between married and unmarried people are the result of healthier people being more likely to marry.
Alternatively, there may be a true causal link between marriage and better health. Marriage could improve health outcomes in a variety of ways. It may result in two incomes, as well as economies of scale, improving economic well-being.
Having more income could, in turn, improve health outcomes by enhancing access to health care or lowering stress. In addition, a spouse may play an important role in monitoring and encouraging healthy behaviors (such as good eating habits and regular exercise), as well as in discouraging unhealthy ones (such as smoking or heavy drinking). Marriage may also provide an emotionally fulfilling, intimate relationship, satisfying the need for social connection, which could have implications for both physical and mental health. Most researchers conclude that the association between marriage and health represents a combination of the selection of healthier people into marriage and true health benefits from marriage.
Measuring the Effects of Marriage
Because marriage is likely to be both a cause and a consequence of health outcomes, research must disentangle the influence of selection from the true causal influence of marriage. Distinguishing between these two factors requires careful analysis and advanced statistical methods that have been absent from many studies.
The studies providing the strongest evidence use longitudinal data and examine the association between changes in health outcomes and transitions into and out of marriage. Studies of this type provide more convincing evidence of a causal relationship between marriage and health because sample members serve as their own control group, and the effect of marriage is measured by comparing their outcomes before and after marriage. This method avoids comparing two groups that may have different background characteristics in particular, people who marry and people who do not which may lead to misleading and inaccurate results.
Some health outcomes are not well suited for this type of analysis, however. For example, many physical health outcomes cannot be examined in this way, because changes can unfold over a long time and may not be apparent immediately after a marital transition.
Effects on Health Behaviors
Marriage may influence health through its effect on behaviors such as alcohol consumption, drug use, cigarette smoking, diet, and exercise. Recent research suggests that marriage has significant effects on the health behaviors of both men and women, but the pattern is mixed marriage is associated with healthier behaviors in some cases and less healthy behaviors in others. Studies consistently indicate that marriage reduces heavy drinking and overall alcohol consumption, and that effects are similar for young men and young women, and for both African Americans and whites. Although the research is less extensive, marriage is also associated with reduced marijuana use for young men, but less so for women. Less is known about the effects of marriage on the substance use of older adults. Studies of marriage and smoking reveal no consistent pattern of results, suggesting that marriage may have little or no influence on this behavior.
In contrast to studies of alcohol and drug use, studies of the effect of marriage on weight and physical activity suggest that marriage may have negative effects on healthy behaviors and may encourage a more sedentary lifestyle. Several rigorous studies find that marriage leads to modest weight increases for both men and women; typically averaging less than five pounds. The research on the effects of marriage on physical activity is less conclusive because it is not based on longitudinal analysis and does not fully adjust for differences between those who marry and those who do not. The evidence that is available suggests marriage may lead to reductions in physical activity, particularly for men.
For certain health behaviors in particular, substance use among younger adults and weight gain among all adults the influence of marriage has been well studied and is well understood. For other behaviors, less is known and additional research is needed before stronger conclusions can be drawn.
Effects on Health Care Access, Use, and Costs
Marriage may influence physical health through its effects on health care access and use. Studies of the link between marriage and health insurance suggest that by offering access to coverage through a spouse’s policy marriage increases the likelihood of having insurance and reduces the likelihood of becoming uninsured after a job loss or other major life event. Limited evidence also suggests that marriage may increase the use of preventive care such as cancer screenings.
Because of its effects on health care use, marriage is also associated with lower health care costs among older adults. For example, studies show that, because marriage reduces the risk of nursing home admission, marriage may also lead to reduced nursing home costs. The effect of marriage in shortening hospital stays may also lead to reductions in health care costs. Research indicates that the effect of marriage on health care costs exists independent of the effect of marriage on physical health. Specifically, many married people rely on their spouses for informal care, and thus require fewer long hospital stays and nursing home admissions, resulting in lower health care costs even if married and unmarried older adults are equally likely to get sick. These studies find that wives are especially likely to provide informal care for their husbands at home, so the effect of marriage on health care costs may be larger for men.
Effects on Mental Health
Marriage may affect many aspects of mental health. The most recent rigorous research suggests that marriage reduces depressive symptoms for both men and women. In particular, these studies find that getting married decreases depressive symptoms, while getting divorced increases them. Research has also documented that increases in depressive symptoms after divorce are long-lasting and that the prevalence of these symptoms remains elevated years after the marital breakup. In addition, studies comparing the mental health of stably married adults to those who remain unmarried find that those who are stably married have fewer depressive symptoms (and smaller increases in these symptoms as they grow older), even after controlling for baseline mental health.
Effects on Physical Health and Longevity
Many studies have documented that people who marry live longer and enjoy better physical health than those who do not marry. However, methodological issues require caution in interpreting this pattern, because most of the research in this area relies on descriptive methods that do not adequately control for the possible selection of healthier people into marriage. Although central to the overall assessment of the link between marriage and health, rigorous research evidence concerning the effect of marriage on specific physical health outcomes is limited, and few solid conclusions can be drawn.
The rigorous research currently available provides limited evidence of an effect of marriage on physical health. Recent research finds a significant positive effect of marriage on how men rate their overall physical health status; however, it finds no such effect for women. Researchers find a positive effect on women’s physical health, as measured by the prevalence of specific health conditions and illnesses. However, no recent rigorous studies based on U.S. samples have examined whether a similar marriage effect on the frequency of health conditions or illnesses exists among men. Similarly, little evidence exists on the links between marriage and specific health conditions or diseases. One exception is a recent study that suggests a possible link between marriage and the risk of cardiovascular disease for women; however, the study finds no such effect for men. Overall, the existing research evidence on the links between marriage and physical health is limited to a narrow range of health measures and does not offer a complete picture of the influence of marriage on physical health.
Many studies have pointed to a strong relationship between marriage and longevity, but this research also has limitations. In particular, these studies are typically limited to simple descriptive comparisons of married and unmarried adults that do not adequately distinguish the effect of marriage from the possible effects of healthier people selecting into marriage. As noted, the most reliable studies of links between marriage and health examine measures directly before and after marital transitions. However, because longevity is determined only at the end of life, it is not possible to observe how a marital transition changes longevity.
Intergenerational Health Effects
An emerging literature on the possible intergenerational health effects of marriage suggests that marriage also has potential long-term consequences for the physical health of a couple’s children. In particular, studies show that growing up with married parents is associated with better physical health in adulthood and increased longevity. Research suggests that such intergenerational health effects are especially strong for men and operate equally for African American and white men. There is less evidence examining possible differences in this relationship for African American and white women.
There are many possible reasons why parental marital status may have long-term health consequences for children. However, existing research provides limited evidence on the pathways by which childhood family structure affects adult physical health and longevity. Several studies suggest that the effects work mostly through the role of childhood family structure in shaping children’s future socioeconomic attainment, and through adult health risk behaviors, such as smoking and heavy drinking. On average, children raised in two-parent families obtain more education and exhibit healthier adult behaviors than children from other types of families. These differences, in turn, have consequences for adult health and longevity.
Research on intergenerational health effects has focused on trends for people born in the late 19th and early 20th centuries, a period when patterns of marriage, divorce, and single parenthood were much different from today. It is possible that the apparent benefits of marriage for children’s health have weakened as single parenthood and divorce have become more common and less stigmatizing. In addition, much of the research is limited to data for small nonrepresentative samples. The available nationally representative evidence is based on data sets that began tracking sample members as adults, which limits the ability to control for differences in the background characteristics of those who grew up in a two-parent family and those who did not.
Sources
What is a “healthy marriage?: Why Marriage Matters, Second Edition: Twenty-Six Conclusions from the Social Sciences, September 2005, www.acf.hhs.gov/healthymarriage/about/mission.html#background.
Marital Status and Health: United States, 1999–2002: Marital Status and Health: United States, 1999–2002 , Centers for Disease Control and Prevention, //http://www.cdc.gov/nchs/pressroom/04facts/marriedadults.htm//
The Effects of Marriage on Health: The Effects of Marriage on Health, A Synthesis of Recent Research Evidence , U.S. Department of Health and Human Services, Office of the Assistant Secretary for Planning and Evaluation, Office of Human Services Policy, June 2007, http://aspe.hhs.gov/hsp/07/marriageonhealth/rb.htm .


3.2: Hazard Concepts
Concepts
Globally Harmonized System
To best classify hazards, the concept of GHS (Globally Harmonized System) has been introduced. Figure \(\PageIndex{1}\) demonstrates the categories of hazards:
Notice that each logo attempts to demonstrate pictorially the type of hazard represented by a specific chemical or material. For example, notice Figure \(\PageIndex{2}\) below. This particular chemical’s hazard level could be listed as “gases under pressure” and “explosives”. The intensity of its peculiar hazards is evaluated according to the pressure and the explosive nature of the gas.
Exposure and Categories of Hazardous Substances
Our overall sensitivity to hazards, again, depends on a number of factors that not only include the typical factors of levels, LDs, type of toxin, modality, etc., but also to our idiosyncratic immunity or responsiveness.
We have been accustomed to a number of wonderful creature comforts in life that have only come about because of the power, versatility, and creativity inherent in the chemical enterprise. For example, phosgene, a notorious chemical warfare agent in the Great War, is now used as a precursor for the manufacture of a number of items including polyurethane. Shown below in Figure \(\PageIndex{3}\) is a representation of phosgene:
Lab Safety
Lab safety is an essential part of working with hazardous materials. It is important to follow good lab practice techniques and to know how to deal with situations should they occur. In the following video by Chemistry crash courses, some good lab techniques and safety guidelines are discussed. Lab Techniques and safety by crash course: https://www.youtube.com/watch?v=VRWRmIEHr3A
Reference: Green, H. Crashcourse. (2013, July 8). Lab Techniques & Safetey: Crash Course Chemistry#21. Retrieved from https://www.youtube.com/watch?v=VRWRmIEHr3A
Lethal Dose
Lethal dose (LD50) is the amount of any ingested or interfering substance that kills 50% of a test 58 sample. It is expressed in mg/kg, or milligrams of substance per kilogram of body weight. In toxicology, it is also referred to as the median lethal dose that refers specifically to a toxin, radiation, or pathogen. The lower the LD50, the more toxic is the item being measured for toxicity. It can be considered a pragmatic approach to toxicity exposure levels because in general, toxicity does NOT always scale with body mass. The choice of 50% lethality as the gold standard avoids ambiguity because it measures in the extremes and reduces the amount of testing. However, such a fact also means that LD50 is not the lethal dose for all subjects; in other words, some may be killed by much less. Measures such as “LD1” and “LD99” (dosages required to kill 1% or 99%, respectively, of the test population) are sometimes used. Shown below is a chart of sample LD50 taken from Wikipedia (en.Wikipedia.org/wiki/Median_lethal_dose) with active links to allow further investigation of the substances whose measurements are given.
|
Substance |
LD 50 (LC 50 ) |
LD 50 : g/kg (LC 50 g/L) standardized |
|
Water |
>90 g/kg |
>90 |
| Pentaborane | <50 mg/kg | <0.05 |
| Cobalt(II)chloride | 80 mg/kg | 0.08 |
| Metallic Arsenic | 763 mg/kg | 0.763 |
| Cadmium oxide | 72 mg/kg | 0.072 |
| Sucrose (table sugar) | 29,700 mg/kg | 29.7 |
| Monosodium glutamate (MSG) | 16,600 mg/kg | 16.6 |
| Vitamin C (ascorbic acid) | 11,900 mg/kg | 11.9 |
| Urea | 8,471 mg/kg | 8.471 |
| Cyanuric acid | 7,700 mg/kg | 7.7 |
| Cadmium sulfide | 7,080 mg/kg | 7.08 |
| ethanol (grain alcohol) | 7,060 mg/kg | 7.06 |
| sodium isopropyl methylphosphonic acid (IMPA, metabolite of sarin) |
6,860 mg/kg |
6.86 |
| Melamine | 6,000 mg/kg | 6.00 |
| Melamine cyanurate | 4,100 mg/kg | 4.1 |
| Venom of Brazilian Wandering Spider | 134 µg/kg | 0.000134 |
| Venom of Inland Taipan (Australian snake) | 25 µg/kg | 0.000025 |
| Ricin |
22 µg/kg 22-30 mg/kg |
0.000022 0.02 |
| 2,3,7,8- Tetrachlorodibenzodioxin (TCD-D, a dioxin) | 20 µg/kg | 0.000002 |
Sources for toxicity information:
- http://www.atsdr.cdc.gov/
- http://cfpub.epa.gov/ecotox/
- toxnet.nlm.nih.gov/
Notice that the venom of the Brazilian Wandering Spider is particularly potent.  Luckily the venom discharged per bite is quite small. Nevertheless, the point is that the vector (or venom) represents a toxin that is of sufficient lethality that it can cause great harm or injury to a human being.


2.1: Orders of magnitude
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Although you should try to fight intuition when building a model to describe a particular phenomenon, you should not abandon critical thinking and should always ask if a prediction from your model makes sense. One of the most straightforward ways to estimate if a model makes sense is to ask whether it predicts the correct order of magnitude for a quantity. Usually, the order of magnitude for a quantity can be determined by making a very simple model, ideally one that you can work through in your head. When we say that a prediction gives the right “order of magnitude”, we usually mean that the prediction is within a factor of “a few” (up to a factor of 10) of the correct answer. For example, if a measurement gives a value of 2000, then we would consider that a model prediction of 8,000 gave the right order of magnitude (it differs from the correct answer by a factor of 4, whereas a prediction of 24,000 would not (it differs by a factor of 12).
Example \(\PageIndex{1}\)
How many ping pong balls can you fit into a school bus? Is it of order \(10,000\), or \(100,000\), or more?
Solution
Our strategy is to estimate the volumes of a school bus and of a ping pong ball, and then calculate how many times the volume of the ping pong ball fits into the volume of the school bus.
We can model a school bus as a box, say \(20\:\text{m}×2\:\text{m}×2\:\text{m}\), with a volume of \(80\:\text{m}^{3}∼100\:\text{m}^{3}\).
We can model a ping pong ball as a sphere with a diameter of \(0.03\) m \((3\:\text{cm})\). When stacking the ping pong balls, we can model them as little cubes with a side given by their diameter, so the volume of a ping pong ball, for stacking, is \(∼ 0.00003\:\text{m}^{3}=3×10^{−5}\:\text{m}^{3}\). If we divide \(100\:\text{m}^{3}\) by \(3 × 10^{−5}\:m^{3}\), using scientific notation:
\[\frac{100\:\text{m}^{3}}{3\times\:10^{-5}\text{m}^{3}}=\frac{1\times 10^{2}}{3\times 10^{-5}}=\frac{1}{3}\times 10^{7}\sim 3\times 10^{6}\]
Thus, we expect to be able to fit about three million ping pong balls in a school bus.
Exercise \(\PageIndex{1}\)
Fill in the following table, giving the order of magnitude (in meters) of the sizes of different physical objects. Feel free to look these up on the internet!
| Object | Order of Magnitude |
|---|---|
| Proton | |
| Nucleus of atom | |
| Hydrogen atom | |
| Virus | |
| Human skin cell | |
| Width of human hair | |
| Human | \(1\) m |
| Height of Mt. Everset | |
| Radius of the Earth | |
| Radius of the Sun | |
| Radius of the Milky Way |
- Answer


14.15: The CRAAP Method
- Examine the criteria used in the CRAAP Method
- Use the CRAAP method to analyze the currency, relevance, authority, accuracy, reliability, and purpose of a source
Using the acronym CRAAP, we can carefully evaluate the effectiveness, authority, and credibility of a source. CRAAP stands for currency, relevance, authority, accuracy, and purpose. Let’s take a closer look at each of these pieces below.
Currency: The timeliness of the information
Key Question : When was the item of information published or produced?
Determining when an item of information was published or produced is an aspect of evaluating information. The date information was published or produced tells you how current it is or how contemporaneous it is with the topic you are researching. There are two facets to the issue of currency.
- Is the information the most recent version?
- Is the information the original research, description, or account?
The question of most recent version of information versus an original or primary version can be a critical one. For example: If you were doing a project on the survival of passengers in car crashes, you would need the most recent information on automobile crash tests, structural strength of materials, car wreck mortality statistics, etc. If, on the other hand, you were doing a project on the feelings of college students about the Vietnam War during the 1960s, you would need information written in the 1960s by college students (primary sources) as well as materials written since then about college students in the 1960s (secondary sources). Key indicators of the currency of the information are:
- date of copyright
- date of publication
- date of revision or edition
- dates of sources cited
- date of patent or trademark
Relevance: The importance of the information for your needs
Key Question: How does this source contribute to my research paper?
The discussion of suitability above is essentially the same thing as relevance. When you read through your source, consider how the source will effectively support your argument and how you can utilize the source in your paper. You should also consider whether the source provides sufficient coverage of the topic. Information sources with broad, shallow coverage mean that you need to find other sources of information to obtain adequate details about your topic. Information sources with a very narrow focus or a distinct bias mean that you need to find additional sources to obtain the information on other aspects of your topic. Some questions to consider are:
- Does the information relate to my topic or answer my question?
- Who is the intended audience?
- Is the information at an appropriate level (i.e. not too simple or advanced) for my needs?
- Did I look at a variety of sources before deciding to use this one?
- Would I be comfortable using this source for my college research paper?
Authority: The source of the information
Key Question : Is the person, organization, or institution responsible for the intellectual content of the information knowledgeable in that subject?
Determining the knowledge and expertise of the author of information is an important aspect of evaluating the reliability of information. Anyone can make an assertion or a statement about some thing, event, or idea, but only someone who knows or understands what that thing, event, or idea is can make a reasonably reliable statement or assertion about it. Some external indications of knowledge of or expertise are:
- a formal academic degree in a subject area
- professional or work-related experience–businessmen, government agency personnel, sports figures, etc. have expertise on their area of work
- active involvement in a subject or organization by serious amateurs who spend substantial amounts of personal time researching and studying that subject area.
- organizations, agencies, institutions, corporations with active involvement or work in a particular subject area.
HINT: Be careful of opinions stated by professionals outside of their area of work expertise.
Accuracy: The reliability, truthfulness, and correctness of the information
Key Question : How free from error is this piece of information?
Establishing the accuracy, or relative accuracy, of information is an important part of evaluating the reliability of information. It is easier to establish the accuracy of facts than it is opinions, interpretations, or ideas. The more an idea, opinion, or other piece of information varies from the accepted point of view on a particular topic the harder it is to establish its accuracy. It may be completely accurate but corroborating it is both more necessary and more difficult. An important aspect of accuracy is the intellectual integrity of the item.
- Are the sources appropriately cited in the text and listed in the references?
- Are quotations cited correctly and in context? Out of context quotations can be misleading and sometimes completely erroneous.
- Are there exaggerations, omissions, or errors? These are difficulty to identify if you use only one source of information. Always use several different sources of information on your topic. Analyzing what different sources say about a topic is one way to understand that topic.
In addition to errors of fact and integrity, you need to watch for errors of logic. Errors of logic occur primarily in the presentation of conclusions, opinions, interpretations, editorials, ideas, etc. Some indications that information is accurate are:
- the same information can be found in other reliable sources
- the experiment can be replicated and returns the same results
- the documentation provided in support of the information is substantive
- the sources used for documentation are known to be generally reliable
- the author of the information is known to have expertise on that subject
- the presentation is free from logical fallacies or errors
- quotations are “in context”-the meaning of the original work is kept in the work which quotes the original
- quotations are correctly cited
- acronyms are clearly defined at the beginning
Some indications that information may not be accurate are:
- facts cannot be verified or are contradicted in other sources
- sources used are known to be unreliable or highly biased
- bibliography of sources used is inadequate or non-existent
- quotations are taken out of context and given a different meaning
- acronyms are not defined and the intended audience is a general one
- presence of one or more logical fallacies
- authority cited is another part of the same organization
Purpose: The reason the information exists
Key Question : Who is this information written for or this product developed for?
Identifying the intended audience of the information or product is another aspect of evaluating information. The intended audience of an item generally determines the style of presentation, the level of technical detail, and the depth of coverage. You should also consider the author’s objectivity. Are they trying to persuade? Do they present any bias? While it is unlikely that anything humans do is ever absolutely objective, it is important to establish that the information you intend to use is reasonably objective, or if it is not, to establish exactly what the point of view or bias is. There are times when information expressing a particular point of view or bias is useful, but you must use it consciously. You must know what the point of view is and why that point of view is important to your project. For example , books on food sanitation written for children, for restaurant workers, or for research microbiologists will be very different even though they all cover the same topic.
Determining the intended audience of a particular piece of information will help you decide whether or not the information will be too basic, too technical, too general, or just right for your needs. The intended audience can also indicate the potential reliability of the item because some audiences require more documentation than others.
For example , items produced for scholarly or professional audiences are generally produced by experts and go through a peer evaluation process. Items produced for the mass market frequently are not produced by experts and generally do not go through an evaluation process. Some indications of the intended audience are:
- highly technical language, complex analysis, very sophisticated/technical tools can indicate a technical, professional, or scholarly audience
- how-to information or current practices in “X” are frequently written by experts for practitioners in that field
- substantive and serious presentations of a topic with not too much technical language are generally written for the educated lay audience
- popular language, fairly simple presentations of a topic, little or no analysis, inexpensive tools can indicate a general or popular audience
- bibliographies, especially long bibliographies, are generally compiled by and for those doing research on that topic
Review the steps of the CRAAP method and practice evaluating sources in this tutorial from Eastern Michigan University. Be sure to complete the practice exercises at the end of the tutorial.
Watch this video for a recap of each of the components of the CRAAP method.
You can view the transcript for “How Library Stuff Works: How to Evaluate Resources (the CRAAP test) here (opens in new window) .
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Evaluating Information. Provided by : The University of Rhode Island. Located at : http://uri.libguides.com/start/craap . License : CC BY-SA: Attribution-ShareAlike
- Provided by : Virginia Tech. Located at : http://info-skills.lib.vt.edu/evaluating_info/2.html . Project : University Libraries Information Skills Modules. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- CRAAP Tutorial. Authored by : Bill Marino. Provided by : Eastern Michigan University. Located at : www.emich.edu/library/help/reliability/. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Analyze sources using the CRAAP method image. Authored by : Kim Louie for Lumen Learning. License : CC BY: Attribution
- How Library Stuff Works: How to Evaluate Resources (the CRAAP Test). Authored by : McMaster Libraries. Located at : https://www.youtube.com/watch?time_continue=115&v=_M1-aMCJHFg&feature=emb_logo . License : Other . License Terms : Standard YouTube License