10.4: Using Spectra to Measure Stellar Radius, Composition, and Motion
Learning Objectives
By the end of this section, you will be able to:
- Understand how astronomers can learn about a star’s radius and composition by studying its spectrum
- Explain how astronomers can measure the motion and rotation of a star using the Doppler effect
- Describe the proper motion of a star and how it relates to a star’s space velocity
Analyzing the spectrum of a star can teach us all kinds of things in addition to its temperature. We can measure its detailed chemical composition as well as the pressure in its atmosphere. From the pressure, we get clues about its size. We can also measure its motion toward or away from us and estimate its rotation.
Clues to the Size of a Star
As we shall see in The Stars: A Celestial Census, stars come in a wide variety of sizes. At some periods in their lives, stars can expand to enormous dimensions. Stars of such exaggerated size are called giants. Luckily for the astronomer, stellar spectra can be used to distinguish giants from run-of-the-mill stars (such as our Sun).
 A giant star has a large, extended photosphere. Because it is so large, a giant star’s atoms are spread over a great volume, which means that the density of particles in the star’s photosphere is low. As a result, the pressure in a giant star’s photosphere is also low. This low pressure affects the spectrum in two ways. First, a star with a lower-pressure photosphere shows narrower spectral lines than a star of the same temperature with a higher-pressure photosphere (Figure \(\PageIndex{1}\)). The difference is large enough that careful study of spectra can tell which of two stars at the same temperature has a higher pressure (and is thus more compressed) and which has a lower pressure (and thus must be extended). This effect is due to collisions between particles in the star’s photosphere—more collisions lead to broader spectral lines. Collisions will, of course, be more frequent in a higher-density environment. Think about it like traffic—collisions are much more likely during rush hour, when the density of cars is high.
Second, more atoms are ionized in a giant star than in a star like the Sun with the same temperature. The ionization of atoms in a star’s outer layers is caused mainly by photons, and the amount of energy carried by photons is determined by temperature. But how long atoms stay ionized depends in part on pressure. Compared with what happens in the Sun (with its relatively dense photosphere), ionized atoms in a giant star’s photosphere are less likely to pass close enough to electrons to interact and combine with one or more of them, thereby becoming neutral again. Ionized atoms, as we discussed earlier, have different spectra from atoms that are neutral.
Abundances of the Elements
Absorption lines of a majority of the known chemical elements have now been identified in the spectra of the Sun and stars. If we see lines of iron in a star’s spectrum, for example, then we know immediately that the star must contain iron.
Note that the absence of an element’s spectral lines does not necessarily mean that the element itself is absent. As we saw, the temperature and pressure in a star’s atmosphere will determine what types of atoms are able to produce absorption lines. Only if the physical conditions in a star’s photosphere are such that lines of an element should (according to calculations) be there can we conclude that the absence of observable spectral lines implies low abundance of the element.
Suppose two stars have identical temperatures and pressures, but the lines of, say, sodium are stronger in one than in the other. Stronger lines mean that there are more atoms in the stellar photosphere absorbing light. Therefore, we know immediately that the star with stronger sodium lines contains more sodium. Complex calculations are required to determine exactly how much more, but those calculations can be done for any element observed in any star with any temperature and pressure.
Of course, astronomy textbooks such as ours always make these things sound a bit easier than they really are. If you look at the stellar spectra such as those in Figure \(17.3.3\) in Section 17.3, you may get some feeling for how hard it is to decode all of the information contained in the thousands of absorption lines. First of all, it has taken many years of careful laboratory work on Earth to determine the precise wavelengths at which hot gases of each element have their spectral lines. Long books and computer databases have been compiled to show the lines of each element that can be seen at each temperature. Second, stellar spectra usually have many lines from a number of elements, and we must be careful to sort them out correctly. Sometimes nature is unhelpful, and lines of different elements have identical wavelengths, thereby adding to the confusion. And third, as we saw in the chapter on Radiation and Spectra, the motion of the star can change the observed wavelength of each of the lines. So, the observed wavelengths may not match laboratory measurements exactly. In practice, analyzing stellar spectra is a demanding, sometimes frustrating task that requires both training and skill.
Studies of stellar spectra have shown that hydrogen makes up about three-quarters of the mass of most stars. Helium is the second-most abundant element, making up almost a quarter of a star’s mass. Together, hydrogen and helium make up from 96 to 99% of the mass; in some stars, they amount to more than 99.9%. Among the 4% or less of “heavy elements,” oxygen, carbon, neon, iron, nitrogen, silicon, magnesium, and sulfur are among the most abundant. Generally, but not invariably, the elements of lower atomic weight are more abundant than those of higher atomic weight.
Take a careful look at the list of elements in the preceding paragraph. Two of the most abundant are hydrogen and oxygen (which make up water); add carbon and nitrogen and you are starting to write the prescription for the chemistry of an astronomy student. We are made of elements that are common in the universe—just mixed together in a far more sophisticated form (and a much cooler environment) than in a star.
As we mentioned in The Spectra of Stars (and Brown Dwarfs) section, astronomers use the term “metals” to refer to all elements heavier than hydrogen and helium. The fraction of a star’s mass that is composed of these elements is referred to as the star’s metallicity . The metallicity of the Sun, for example, is 0.02, since 2% of the Sun’s mass is made of elements heavier than helium.
Appendix K lists how common each element is in the universe (compared to hydrogen); these estimates are based primarily on investigation of the Sun, which is a typical star. Some very rare elements, however, have not been detected in the Sun. Estimates of the amounts of these elements in the universe are based on laboratory measurements of their abundance in primitive meteorites, which are considered representative of unaltered material condensed from the solar nebula (see the Cosmic Samples and the Origin of the Solar System chapter).
Radial Velocity
When we measure the spectrum of a star, we determine the wavelength of each of its lines. If the star is not moving with respect to the Sun, then the wavelength corresponding to each element will be the same as those we measure in a laboratory here on Earth. But if stars are moving toward or away from us, we must consider the Doppler effect . We should see all the spectral lines of moving stars shifted toward the red end of the spectrum if the star is moving away from us, or toward the blue (violet) end if it is moving toward us (Figure \(\PageIndex{2}\)). The greater the shift, the faster the star is moving. Such motion, along the line of sight between the star and the observer, is called radial velocity and is usually measured in kilometers per second.
William Huggins, pioneering yet again, in 1868 made the first radial velocity determination of a star. He observed the Doppler shift in one of the hydrogen lines in the spectrum of Sirius and found that this star is moving toward the solar system. Today, radial velocity can be measured for any star bright enough for its spectrum to be observed. As we will see in The Stars: A Celestial Census, radial velocity measurements of double stars are crucial in deriving stellar masses.
Proper Motion
There is another type of motion stars can have that cannot be detected with stellar spectra. Unlike radial motion, which is along our line of sight (i.e., toward or away from Earth), this motion, called proper motion , is transverse : that is, across our line of sight. We see it as a change in the relative positions of the stars on the celestial sphere (Figure \(\PageIndex{3}\)). These changes are very slow. Even the star with the largest proper motion takes 200 years to change its position in the sky by an amount equal to the width of the full Moon, and the motions of other stars are smaller yet.
For this reason, with our naked eyes, we do not notice any change in the positions of the bright stars during the course of a human lifetime. If we could live long enough, however, the changes would become obvious. For example, some 50,000 years from now, terrestrial observers will find the handle of the Big Dipper unmistakably more bent than it is now (Figure \(\PageIndex{4}\)).
We measure the proper motion of a star in arcseconds (1/3600 of a degree) per year. That is, the measurement of proper motion tells us only by how much of an angle a star has changed its position on the celestial sphere. If two stars at different distances are moving at the same velocity perpendicular to our line of sight, the closer one will show a larger shift in its position on the celestial sphere in a year’s time. As an analogy, imagine you are standing at the side of a freeway. Cars will appear to whiz past you. If you then watch the traffic from a vantage point half a mile away, the cars will move much more slowly across your field of vision. In order to convert this angular motion to a velocity, we need to know how far away the star is.
To know the true space velocity of a star—that is, its total speed and the direction in which it is moving through space relative to the Sun—we must know its radial velocity, proper motion, and distance (Figure \(\PageIndex{5}\)). A star’s space velocity can also, over time, cause its distance from the Sun to change significantly. Over several hundred thousand years, these changes can be large enough to affect the apparent brightnesses of nearby stars. Today, Sirius, in the constellation Canis Major (the Big Dog) is the brightest star in the sky, but 100,000 years ago, the star Canopus in the constellation Carina (the Keel) was the brightest one. A little over 200,000 years from now, Sirius will have moved away and faded somewhat, and Vega, the bright blue star in Lyra, will take over its place of honor as the brightest star in Earth’s skies.
Rotation
We can also use the Doppler effect to measure how fast a star rotates. If an object is rotating, then one of its sides is approaching us while the other is receding (unless its axis of rotation happens to be pointed exactly toward us). This is clearly the case for the Sun or a planet; we can observe the light from either the approaching or receding edge of these nearby objects and directly measure the Doppler shifts that arise from the rotation.
Stars, however, are so far away that they all appear as unresolved points. The best we can do is to analyze the light from the entire star at once. Due to the Doppler effect, the lines in the light that come from the side of the star rotating toward us are shifted to shorter wavelengths and the lines in the light from the opposite edge of the star are shifted to longer wavelengths. You can think of each spectral line that we observe as the sum or composite of spectral lines originating from different speeds with respect to us. Each point on the star has its own Doppler shift, so the absorption line we see from the whole star is actually much wider than it would be if the star were not rotating. If a star is rotating rapidly, there will be a greater spread of Doppler shifts and all its spectral lines should be quite broad. In fact, astronomers call this effect line broadening , and the amount of broadening can tell us the speed at which the star rotates (Figure \(\PageIndex{6}\)).
Measurements of the widths of spectral lines show that many stars rotate faster than the Sun, some with periods of less than a day! These rapid rotators spin so fast that their shapes are “flattened” into what we call oblate spheroids . An example of this is the star Vega, which rotates once every 12.5 hours. Vega’s rotation flattens its shape so much that its diameter at the equator is 23% wider than its diameter at the poles (Figure \(\PageIndex{7}\)). The Sun, with its rotation period of about a month, rotates rather slowly. Studies have shown that stars decrease their rotational speed as they age. Young stars rotate very quickly, with rotational periods of days or less. Very old stars can have rotation periods of several months.
As you can see, spectroscopy is an extremely powerful technique that helps us learn all kinds of information about stars that we simply could not gather any other way. We will see in later chapters that these same techniques can also teach us about galaxies, which are the most distant objects that can we observe. Without spectroscopy, we would know next to nothing about the universe beyond the solar system.
ASTRONOMY AND PHILANTHROPY
Throughout the history of astronomy, contributions from wealthy patrons of the science have made an enormous difference in building new instruments and carrying out long-term research projects. Edward Pickering’s stellar classification project, which was to stretch over several decades, was made possible by major donations from Anna Draper. She was the widow of Henry Draper, a physician who was one of the most accomplished amateur astronomers of the nineteenth century and the first person to successfully photograph the spectrum of a star. Anna Draper gave several hundred thousand dollars to Harvard Observatory. As a result, the great spectroscopic survey is still known as the Henry Draper Memorial, and many stars are still referred to by their “HD” numbers in that catalog (such as HD 209458).
In the 1870s, the eccentric piano builder and real estate magnate James Lick (Figure \(\PageIndex{8}\)) decided to leave some of his fortune to build the world’s largest telescope. When, in 1887, the pier to house the telescope was finished, Lick’s body was entombed in it. Atop the foundation rose a 36-inch refractor, which for many years was the main instrument at the Lick Observatory near San Jose.
The Lick telescope remained the largest in the world until 1897, when George Ellery Hale persuaded railroad millionaire Charles Yerkes to finance the construction of a 40-inch telescope near Chicago. More recently, Howard Keck, whose family made its fortune in the oil industry, gave $70 million from his family foundation to the California Institute of Technology to help build the world’s largest telescope atop the 14,000-foot peak of Mauna Kea in Hawaii (see the chapter on Astronomical Instruments to learn more about these telescopes). The Keck Foundation was so pleased with what is now called the Keck telescope that they gave $74 million more to build Keck II, another 10-meter reflector on the same volcanic peak.
Now, if any of you become millionaires or billionaires, and astronomy has sparked your interest, do keep an astronomical instrument or project in mind as you plan your estate. But frankly, private philanthropy could not possibly support the full enterprise of scientific research in astronomy. Much of our exploration of the universe is financed by federal agencies such as the National Science Foundation and NASA in the United States, and by similar government agencies in the other countries. In this way, all of us, through a very small share of our tax dollars, are philanthropists for astronomy.
Summary
Spectra of stars of the same temperature but different atmospheric pressures have subtle differences, so spectra can be used to determine whether a star has a large radius and low atmospheric pressure (a giant star) or a small radius and high atmospheric pressure. Stellar spectra can also be used to determine the chemical composition of stars; hydrogen and helium make up most of the mass of all stars. Measurements of line shifts produced by the Doppler effect indicate the radial velocity of a star. Broadening of spectral lines by the Doppler effect is a measure of rotational velocity. A star can also show proper motion, due to the component of a star’s space velocity across the line of sight.
Glossary
- giant
- a star of exaggerated size with a large, extended photosphere
- proper motion
- the angular change per year in the direction of a star as seen from the Sun
- radial velocity
- motion toward or away from the observer; the component of relative velocity that lies in the line of sight
- space velocity
- the total (three-dimensional) speed and direction with which an object is moving through space relative to the Sun
Contributors and Attributions
-
Andrew Fraknoi (Foothill College), David Morrison (NASA Ames Research Center), Sidney C. Wolff (National Optical Astronomy Observatory) with many 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/astronomy ).


7.1: Solving Trigonometric Equations with Identities
In the last chapter, we solved basic trigonometric equations. In this section, we explore the techniques needed to solve more complicated trig equations. Building from what we already know makes this a much easier task.
Consider the function \(f(x)=2x^{2} +x\). If you were asked to solve \(f(x)=0\), it requires simple algebra:
\[2x^{2} +x=0\nonumber\]Factor
\[x(2x+1)=0\nonumber\]Giving solutions
\[x = 0\text{ or }x = -\dfrac{1}{2}\nonumber\]
Similarly, for \(g(t)=\sin (t)\), if we asked you to solve \(g(t)=0\), you can solve this using unit circle values:
\[\sin (t)=0\text{ for }t=0, \pi , 2\pi\text{ and so on.}\nonumber\]
Using these same concepts, we consider the composition of these two functions:
\[f(g(t))=2(\sin (t))^{2} +(\sin (t))=2\sin ^{2} (t)+\sin (t)\nonumber\]
This creates an equation that is a polynomial trig function. With these types of functions, we use algebraic techniques like factoring and the quadratic formula, along with trigonometric identities and techniques, to solve equations.
As a reminder, here are some of the essential trigonometric identities that we have learned so far:
DefinitionS: IDENTITIES
Pythagorean Identities
\[\cos ^{2} (t)+\sin ^{2} (t)=1\quad 1+\cot ^{2} (t)=\csc ^{2} (t)\quad 1+\tan ^{2} (t)=\sec ^{2} (t)\]
Negative Angle Identities
\[\sin (-t)=-\sin (t)\quad \cos (-t)=\cos (t)\quad \tan (-t)=-\tan (t)\]
\[\csc (-t)=-\csc (t)\quad \sec (-t)=\sec (t)\quad \cot (-t)=-\cot (t)\]
Reciprocal Identities
\[\sec (t)=\dfrac{1}{\cos (t)}\quad \csc (t)=\dfrac{1}{\sin (t)}\quad \tan (t)=\dfrac{\sin (t)}{\cos (t)}\quad \cot (t)=\dfrac{1}{\tan (t)}\]
Example \(\PageIndex{1}\)
Solve \(2\sin ^{2} (t)+\sin (t)=0\) for all solutions with \(0\le t<2\pi\).
Solution
This equation kind of looks like a quadratic equation, but with sin( t ) in place of an algebraic variable (we often call such an equation “quadratic in sine”). As with all quadratic equations, we can use factoring techniques or the quadratic formula. This expression factors nicely, so we proceed by factoring out the common factor of sin(\(t\)):
\[\sin (t)\left(2\sin (t)+1\right)=0\nonumber\]
Using the zero product theorem, we know that the product on the left will equal zero if either factor is zero, allowing us to break this equation into two cases:
\[\sin (t)=0\text{ or }2\sin (t)+1=0\nonumber\]
We can solve each of these equations independently, using our knowledge of special angles.
\[\sin (t)=0\nonumber\]
\[2\sin (t)+1=0\nonumber\]
\[t = 0\text{ or }t = \pi\nonumber\]
\[\sin (t)=-\dfrac{1}{2}\nonumber\]
\[t=\dfrac{7\pi }{6}\text{ or }t=\dfrac{11\pi }{6}\nonumber\]
Together, this gives us four solutions to the equation on \(0\le t<2\pi\):
\[t=0,\pi ,\dfrac{7\pi }{6} ,\dfrac{11\pi }{6}\nonumber\]
We could check these answers are reasonable by graphing the function and comparing the zeros.
Example \(\PageIndex{2}\)
Solve \(3\sec ^{2} (t)-5\sec (t)-2=0\) for all solutions with \(0\le t<2\pi\).
Solution
Since the left side of this equation is quadratic in secant, we can try to factor it, and hope it factors nicely.
If it is easier to for you to consider factoring without the trig function present, consider using a substitution \(u=\sec (t)\), resulting in \(3u^{2} -5u-2=0\), and then try to factor:
\[3u^{2} -5u-2=(3u+1)(u-2)\nonumber\]
Undoing the substitution,
\[(3\sec (t)+1)(\sec (t)-2)=0\nonumber\]
Since we have a product equal to zero, we break it into the two cases and solve each separately.
\[3\sec (t)+1=0\nonumber\]Isolate the secant
\[\sec (t)=-\dfrac{1}{3}\nonumber\]Rewrite as a cosine
\[\dfrac{1}{\cos (t)} =-\dfrac{1}{3}\nonumber\]Invert both sides
\[\cos (t)=-3\nonumber\]
Since the cosine has a range of [-1, 1], the cosine will never take on an output of -3. There are no solutions to this case.
Continuing with the second case,
\[\sec (t)-2=0\nonumber\]Isolate the secant
\[\sec (t)=2\nonumber\]Rewrite as a cosine
\[\dfrac{1}{\cos (t)} =2\nonumber\]Invert both sides
\[\cos (t)=\dfrac{1}{2}\nonumber\]This gives two solutions
\[t=\dfrac{\pi }{3}\text{ or }t=\dfrac{5\pi }{3}\nonumber\]
These are the only two solutions on the interval.
By utilizing technology to graph \(f(t)=3\sec ^{2} (t)-5\sec (t)-2\), a look at a graph confirms there are only two zeros for this function on the interval [0, 2 \(\pi\)), which assures us that we didn’t miss anything.
Exercise \(\PageIndex{1}\)
Solve \(2\sin ^{2} (t)+3\sin (t)+1=0\) for all solutions with \(0\le t<2\pi\).
- Answer
-
Factor as \[\left(2\sin (t)+1\right)\left(\sin (t)+1\right)=0\nonumber\]
\[2\sin (t)+1=0\text{ at }t=\dfrac{7\pi }{6} ,\dfrac{11\pi }{6}\nonumber\]
\[\sin (t)+1=0\text{ at }t=\dfrac{3\pi }{2}\nonumber\]
\[t=\dfrac{7\pi }{6} ,\dfrac{3\pi }{2} ,\dfrac{11\pi }{6}\nonumber\]
When solving some trigonometric equations, it becomes necessary to first rewrite the equation using trigonometric identities. One of the most common is the Pythagorean Identity, \(\sin ^{2} (\theta )+\cos ^{2} (\theta )=1\) which allows you to rewrite \(\sin ^{2} (\theta )\) in terms of \(\cos ^{2} (\theta )\) or vice versa,
IDENTITIES
Alternate Forms of the Pythagorean Identity
\[\begin{array}{l} {\sin ^{2} (\theta )=1-\cos ^{2} (\theta )} \\ {\cos ^{2} (\theta )=1-\sin ^{2} (\theta )} \end{array}\]
These identities become very useful whenever an equation involves a combination of sine and cosine functions.
Example \(\PageIndex{3}\)
Solve \(2\sin ^{2} (t)-\cos (t)=1\) for all solutions with \(0\le t<2\pi\).
Solution
Since this equation has a mix of sine and cosine functions, it becomes more complicated to solve. It is usually easier to work with an equation involving only one trig function. This is where we can use the Pythagorean Identity.
\[2\sin ^{2} (t)-\cos (t)=1\nonumber\]Using \(\sin ^{2} (\theta )=1-\cos ^{2} (\theta )\)
\[2\left(1-\cos ^{2} (t)\right)-\cos (t)=1\nonumber\]Distributing the 2
\[2-2\cos ^{2} (t)-\cos (t)=1\nonumber\]
Since this is now quadratic in cosine, we rearrange the equation so one side is zero and factor.
\[-2\cos ^{2} (t)-\cos (t)+1=0\nonumber\]Multiply by -1 to simplify the factoring
\[2\cos ^{2} (t)+\cos (t)-1=0\nonumber\]Factor
\[\left(2\cos (t)-1\right)\left(\cos (t)+1\right)=0\nonumber\]
This product will be zero if either factor is zero, so we can break this into two separate cases and solve each independently.
\[2\cos (t)-1=0\text{ or }\cos (t)+1=0\nonumber\]
\[\cos (t)=\dfrac{1}{2}\text{ or }\cos (t)=-1\nonumber\]
\[t=\dfrac{\pi }{3}\text{ or }t=\dfrac{5\pi }{3}\text{ or }t=\pi\nonumber\]
Exercise \(\PageIndex{3}\)
Solve \(2\sin ^{2} (t)=3\cos (t)\) for all solutions with \(0\le t<2\pi\).
- Answer
-
\[2\left(1-\cos ^{2} (t)\right)=3\cos (t)\nonumber\]
\[2\cos ^{2} (t)+3\cos (t)-2=0\nonumber\]
\[\left(2\cos (t)-1\right)\left(\cos (t)+2\right)=0\nonumber\]
\(\cos (t)+2=0\) has no solutions \(2\cos (t)-1=0\) at \(t=\dfrac{\pi }{3} ,\dfrac{5\pi }{3}\)
In addition to the Pythagorean Identity, it is often necessary to rewrite the tangent, secant, cosecant, and cotangent as part of solving an equation.
Example \(\PageIndex{4}\)
Solve \(\tan (x)=3\sin (x)\) for all solutions with \(0\le x<2\pi\).
Solution
With a combination of tangent and sine, we might try rewriting tangent
\[\tan (x)=3\sin (x)\nonumber\]
\[\dfrac{\sin (x)}{\cos (x)} =3\sin (x)\nonumber\]Multiplying both sides by cosine
\[\sin (x)=3\sin (x)\cos (x) \nonumber\]
At this point, you may be tempted to divide both sides of the equation by sin(\(x\)).
Resist the urge . When we divide both sides of an equation by a quantity, we are assuming the quantity is never zero. In this case, when sin(\(x\)) = 0 the equation is satisfied, so we’d lose those solutions if we divided by the sine.
To avoid this problem, we can rearrange the equation so that one side is zero (You technically can divide by sin( x ), as long as you separately consider the case where sin( x ) = 0. Since it is easy to forget this step, the factoring approach used in the example is recommended.).
\[\sin (x)-3\sin (x)\cos (x)=0\nonumber\]Factoring out sin(\(x\)) from both parts
\[\sin (x)\left(1-3\cos (x)\right)=0 \nonumber\]
From here, we can see we get solutions when \(\sin (x)=0\) or \(1-3\cos (x)=0\).
Using our knowledge of the special angles of the unit circle,
\[\sin (x)=0\text{ when }x = 0\text{ or }x = \pi\nonumber\]
For the second equation, we will need the inverse cosine.
\[1-3\cos (x)=0\nonumber\]
\[\cos (x)=\dfrac{1}{3}\nonumber\]Using our calculator or technology
\[x=\cos ^{-1} \left(\dfrac{1}{3} \right)\approx 1.231\nonumber\]Using symmetry to find a second solution
\[x=2\pi -1.231=5.052 \nonumber\]
We have four solutions on \(0 \le x<2\pi\):
\[x = 0, 1.231, \quad\pi , 5.052\nonumber\]
Example \(\PageIndex{3}\)
Solve \(\sec (\theta )=2\cos (\theta )\) to find the first four positive solutions.
- Answer
-
\[\dfrac{1}{\cos (\theta )} =2\cos (\theta )\nonumber\]
\[\dfrac{1}{2} =\cos ^{2} (\theta )\nonumber\]
\[\cos (\theta )=\pm \sqrt{\dfrac{1}{2} } =\pm \dfrac{\sqrt{2} }{2}\nonumber\]
\[\theta =\dfrac{\pi }{4} ,\dfrac{3\pi }{4} ,\dfrac{5\pi }{4} ,\dfrac{7\pi }{4}\nonumber\]
Example \(\PageIndex{5}\)
Solve \(\dfrac{4}{\sec ^{2} (\theta )} +3\cos \left(\theta \right)=2\cot \left(\theta \right)\tan \left(\theta \right)\) for all solutions with \(0\le \theta <2\pi\).
Solution
\[\dfrac{4}{\sec ^{2} (\theta )} +3\cos \left(\theta \right)=2\cot \left(\theta \right)\tan \left(\theta \right)\nonumber\] Using the reciprocal identities
\[4\cos ^{2} (\theta )+3\cos (\theta )=2\dfrac{1}{\tan (\theta )} \tan (\theta )\nonumber\] Simplifying
\[4\cos ^{2} \left(\theta \right)+3\cos \left(\theta \right)=2\nonumber\] Subtracting 2 from each side
\[4\cos ^{2} \left(\theta \right)+3\cos \left(\theta \right)-2=0\nonumber\]
This does not appear to factor nicely so we use the quadratic formula, remembering that we are solving for cos( \(\theta\) ).
\[\cos (\theta )=\dfrac{-3\pm \sqrt{3^{2} -4(4)(-2)} }{2(4)} =\dfrac{-3\pm \sqrt{41} }{8}\nonumber\]
Using the negative square root first,
\[\cos (\theta )=\dfrac{-3-\sqrt{41} }{8} =-1.175\nonumber\]
This has no solutions, since the cosine can’t be less than -1.
Using the positive square root,
\[\cos (\theta )=\dfrac{-3+\sqrt{41} }{8} =0.425\nonumber\]
\[\theta =\cos ^{-1} \left(0.425\right)=1.131\nonumber\] By symmetry, a second solution can be found
\[\theta =2\pi -1.131=5.152\nonumber\]
Important Topics of This Section
- Review of Trig Identities
- Solving Trig Equations
- By Factoring
- Using the Quadratic Formula
- Utilizing Trig Identities to simplify


20.1: Practical Applications of Monoclonal and Polyclonal Antibodies
- Compare the method of development, use, and characteristics of monoclonal and polyclonal antibodies
- Explain the nature of antibody cross-reactivity and why this is less of a problem with monoclonal antibodies
In an unfortunate incident, a healthcare worker struggling with addiction was caught stealing syringes of painkillers and replacing them with syringes filled with unknown substances. The hospital immediately fired the employee and had him arrested; however, two patients that he had worked with later tested positive for HIV.
While there was no proof that the infections originated from the tainted syringes, the hospital’s public health physician took immediate steps to determine whether any other patients had been put at risk. Although the worker had only been employed for a short time, it was determined that he had come into contact with more than 1300 patients. The hospital decided to contact all of these patients and have them tested for HIV.
- Why does the hospital feel it is necessary to test every patient for HIV?
- What types of tests can be used to determine if a patient has HIV?
In addition to being crucial for our normal immune response, antibodies provide powerful tools for research and diagnostic purposes. The high specificity of antibodies makes them an excellent tool for detecting and quantifying a broad array of targets, from drugs to serum proteins to microorganisms. With in vitro assays, antibodies can be used to precipitate soluble antigens, agglutinate (clump) cells, opsonize and kill bacteria with the assistance of complement, and neutralize drugs, toxins, and viruses.
An antibody’s specificity results from the antigen-binding site formed within the variable regions—regions of the antibody that have unique patterns of amino acids that can only bind to target antigens with a molecular sequence that provides complementary charges and noncovalent bonds. There are limitations to antibody specificity, however. Some antigens are so chemically similar that cross-reactivity occurs; in other words, antibodies raised against one antigen bind to a chemically similar but different antigen. Consider an antigen that consists of a single protein with multiple epitopes (Figure \(\PageIndex{1}\)). This single protein may stimulate the production of many different antibodies, some of which may bind to chemically identical epitopes on other proteins.
Cross-reactivity is more likely to occur between antibodies and antigens that have low affinity or avidity. Affinity, which can be determined experimentally, is a measure of the binding strength between an antibody's binding site and an epitope, whereas avidity is the total strength of all the interactions in an antibody-antigen complex (which may have more than one bonding site). Avidity is influenced by affinity as well as the structural arrangements of the epitope and the variable regions of the antibody. If an antibody has a high affinity/avidity for a specific antigen, it is less likely to cross-react with an antigen for which it has a lower affinity/avidity.
- What property makes antibodies useful for research and clinical diagnosis?
- What is cross-reactivity and why does it occur?
Producing Polyclonal Antibodies
Antibodies used for research and diagnostic purposes are often obtained by injecting a lab animal such as a rabbit or a goat with a specific antigen. Within a few weeks, the animal’s immune system will produce high levels of antibodies specific for the antigen. These antibodies can be harvested in an antiserum, which is whole serum collected from an animal following exposure to an antigen. Because most antigens are complex structures with multiple epitopes, they result in the production of multiple antibodies in the lab animal. This so-called polyclonal antibody response is also typical of the response to infection by the human immune system. Antiserum drawn from an animal will thus contain antibodies from multiple clones of B cells, with each B cell responding to a specific epitope on the antigen (Figure \(\PageIndex{2}\)).
Lab animals are usually injected at least twice with antigen when being used to produce antiserum. The second injection will activate memory cells that make class IgG antibodies against the antigen. The memory cells also undergo affinity maturation, resulting in a pool of antibodies with higher average affinity. Affinity maturation occurs because of mutations in the immunoglobulin gene variable regions, resulting in B cells with slightly altered antigen-binding sites. On re-exposure to the antigen, those B cells capable of producing antibody with higher affinity antigen-binding sites will be stimulated to proliferate and produce more antibody than their lower-affinity peers. An adjuvant, which is a chemical that provokes a generalized activation of the immune system that stimulates greater antibody production, is often mixed with the antigen prior to injection.
Antiserum obtained from animals will not only contain antibodies against the antigen artificially introduced in the laboratory, but it will also contain antibodies to any other antigens to which the animal has been exposed during its lifetime. For this reason, antisera must first be “purified” to remove other antibodies before using the antibodies for research or diagnostic assays.
Clinical Uses of Polyclonal Antisera
Polyclonal antisera are used in many clinical tests that are designed to determine whether a patient is producing antibodies in response to a particular pathogen. While these tests are certainly powerful diagnostic tools, they have their limitations, because they are an indirect means of determining whether a particular pathogen is present. Tests based on a polyclonal response can sometimes lead to a false-positive result—in other words, a test that confirms the presence of an antigen that is, in fact, not present. Antibody-based tests can also result in a false-negative result, which occurs when the test fails to detect an antibody that is, in fact, present.
The accuracy of antibody tests can be described in terms of test sensitivity and test specificity. Test sensitivity is the probability of getting a positive test result when the patient is indeed infected. If a test has high sensitivity, the probability of a false negative is low. Test specificity, on the other hand, is the probability of getting a negative test result when the patient is not infected. If a test has high specificity, the probability of a false positive is low.
False positives often occur due to cross-reactivity, which can occur when epitopes from a different pathogen are similar to those found on the pathogen being tested for. For this reason, antibody-based tests are often used only as screening tests; if the results are positive, other confirmatory tests are used to make sure that the results were not a false positive.
For example, a blood sample from a patient suspected of having hepatitis C can be screened for the virus using antibodies that bind to antigens on hepatitis C virus. If the patient is indeed infected with hepatitis C virus, the antibodies will bind to the antigens, yielding a positive test result. If the patient is not infected with hepatitic C virus, the antibodies will generally not bind to anything and the test should be negative; however, a false positive may occur if the patient has been previously infected by any of a variety of pathogens that elicit antibodies that cross-react with the hepatitis C virus antigens. Antibody tests for hepatitis C have high sensitivity (a low probability of a false negative) but low specificity (a high probability of a false positive). Thus, patients who test positive must have a second, confirmatory test to rule out the possibility of a false positive. The confirmatory test is a more expensive and time-consuming test that directly tests for the presence of hepatitis C viral RNA in the blood. Only after the confirmatory test comes back positive can the patient be definitively diagnosed with a hepatitis C infection. Antibody-based tests can result in a false negative if, for any reason, the patient’s immune system has not produced detectable levels of antibodies. For some diseases, it may take several weeks following infection before the immune system produces enough antibodies to cross the detection threshold of the assay. In immunocompromised patients, the immune system may not be capable of producing a detectable level of antibodies.
Another limitation of using antibody production as an indicator of disease is that antibodies in the blood will persist long after the infection has been cleared. Depending on the type of infection, antibodies will be present for many months; sometimes, they may be present for the remainder of the patient’s life. Thus, a positive antibody-based test only means that the patient was infected at some point in time; it does not prove that the infection is active.
In addition to their role in diagnosis, polyclonal antisera can activate complement, detect the presence of bacteria in clinical and food industry settings, and perform a wide array of precipitation reactions that can detect and quantify serum proteins, viruses, or other antigens. However, with the many specificities of antibody present in a polyclonal antiserum, there is a significant likelihood that the antiserum will cross-react with antigens to which the individual was never exposed. Therefore, we must always account for the possibility of false-positive results when working with a polyclonal antiserum.
- What is a false positive and what are some reasons that false positives occur?
- What is a false negative and what are some reasons that false positives occur?
- If a patient tests negative on a highly sensitive test, what is the likelihood that the person is infected with the pathogen?
Producing Monoclonal Antibodies
Some types of assays require better antibody specificity and affinity than can be obtained using a polyclonal antiserum. To attain this high specificity, all of the antibodies must bind with high affinity to a single epitope. This high specificity can be provided by monoclonal antibodies (mAbs). Table \(\PageIndex{1}\) compares some of the important characteristics of monoclonal and polyclonal antibodies.
Unlike polyclonal antibodies, which are produced in live animals, monoclonal antibodies are produced in vitro using tissue-culture techniques. mAbs are produced by immunizing an animal, often a mouse, multiple times with a specific antigen. B cells from the spleen of the immunized animal are then removed. Since normal B cells are unable to proliferate forever, they are fused with immortal, cancerous B cells called myeloma cells, to yield hybridoma cells. All of the cells are then placed in a selective medium that allows only the hybridomas to grow; unfused myeloma cells cannot grow, and any unfused B cells die off. The hybridomas, which are capable of growing continuously in culture while producing antibodies, are then screened for the desired mAb. Those producing the desired mAb are grown in tissue culture; the culture medium is harvested periodically and mAbs are purified from the medium. This is a very expensive and time-consuming process. It may take weeks of culturing and many liters of media to provide enough mAbs for an experiment or to treat a single patient. mAbs are expensive (Figure \(\PageIndex{3}\)).
| Monoclonal Antibodies | Polyclonal Antibodies |
|---|---|
| Expensive production | Inexpensive production |
| Long production time | Rapid production |
| Large quantities of specific antibodies | Large quantities of nonspecific antibodies |
| Recognize a single epitope on an antigen | Recognize multiple epitopes on an antigen |
| Production is continuous and uniform once the hybridoma is made | Different batches vary in composition |
Clinical Uses of Monoclonal Antibodies
Since the most common methods for producing monoclonal antibodies use mouse cells, it is necessary to create humanized monoclonal antibodies for human clinical use. Mouse antibodies cannot be injected repeatedly into humans, because the immune system will recognize them as being foreign and will respond to them with neutralizing antibodies. This problem can be minimized by genetically engineering the antibody in the mouse B cell. The variable regions of the mouse light and heavy chain genes are ligated to human constant regions, and the chimeric gene is then transferred into a host cell. This allows production of a mAb that is mostly “human” with only the antigen-binding site being of mouse origin.
Humanized mAbs have been successfully used to treat cancer with minimal side effects. For example, the humanized monoclonal antibody drug Herceptin has been helpful for the treatment of some types of breast cancer. There have also been a few preliminary trials of humanized mAb for the treatment of infectious diseases, but none of these treatments are currently in use. In some cases, mAbs have proven too specific to treat infectious diseases, because they recognize some serovars of a pathogen but not others. Using a cocktail of multiple mAbs that target different strains of the pathogen can address this problem. However, the great cost associated with mAb production is another challenge that has prevented mAbs from becoming practical for use in treating microbial infections. 1
One promising technology for inexpensive mAbs is the use of genetically engineered plants to produce antibodies (or plantibodies). This technology transforms plant cells into antibody factories rather than relying on tissue culture cells, which are expensive and technically demanding. In some cases, it may even be possible to deliver these antibodies by having patients eat the plants rather than by extracting and injecting the antibodies. For example, in 2013, a research group cloned antibody genes into plants that had the ability to neutralize an important toxin from bacteria that can cause severe gastrointestinal disease. 2 Eating the plants could potentially deliver the antibodies directly to the toxin.
- How are humanized monoclonal antibodies produced?
- What does the “monoclonal” of monoclonal antibodies mean?
During the 2014–2015 Ebola outbreak in West Africa, a few Ebola-infected patients were treated with ZMapp, a drug that had been shown to be effective in trials done in rhesus macaques only a few months before. 3 ZMapp is a combination of three mAbs produced by incorporating the antibody genes into tobacco plants using a viral vector. By using three mAbs, the drug is effective across multiple strains of the virus. Unfortunately, there was only enough ZMapp to treat a tiny number of patients.
While the current technology is not adequate for producing large quantities of ZMapp, it does show that plantibodies—plant-produced mAbs—are feasible for clinical use, potentially cost effective, and worth further development. The last several years have seen an explosion in the number of new mAb-based drugs for the treatment of cancer and infectious diseases; however, the widespread use of such drugs is currently inhibited by their exorbitant cost, especially in underdeveloped parts of the world, where a single dose might cost more than the patient’s lifetime income. Developing methods for cloning antibody genes into plants could reduce costs dramatically.
Key Concepts and Summary
- Antibodies bind with high specificity to antigens used to challenge the immune system, but they may also show cross-reactivity by binding to other antigens that share chemical properties with the original antigen.
- Injection of an antigen into an animal will result in a polyclonal antibody response in which different antibodies are produced that react with the various epitopes on the antigen.
- Polyclonal antisera are useful for some types of laboratory assays, but other assays require more specificity. Diagnostic tests that use polyclonal antisera are typically only used for screening because of the possibility of false-positive and false-negative results.
- Monoclonal antibodies provide higher specificity than polyclonal antisera because they bind to a single epitope and usually have high affinity .
- Monoclonal antibodies are typically produced by culturing antibody-secreting hybridomas derived from mice. mAbs are currently used to treat cancer, but their exorbitant cost has prevented them from being used more widely to treat infectious diseases. Still, their potential for laboratory and clinical use is driving the development of new, cost-effective solutions such as plantibodies .
Footnotes
- 1 Saylor, Carolyn, Ekaterina Dadachova and Arturo Casadevall, “Monoclonal Antibody-Based Therapies for Microbial Diseases,” Vaccine 27 (2009): G38-G46.
- 2 Nakanishi, Katsuhiro et al., “Production of Hybrid-IgG/IgA Plantibodies with Neutralizing Activity against Shiga Toxin 1,” PloS One 8, no. 11 (2013): e80712.
- 3 Qiu, Xiangguo et al., “Reversion of Advanced Ebola Virus Disease in Nonhuman Primates with ZMapp,” Nature 514 (2014): 47–53.


11.1.1C: Legal Definition of Race
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Many governments provide legal definitions of race for purposes of census-taking and calculating budgets for governmental programs.
Learning Objectives
- Paraphrase the legal definition of race and how it is used in government and law enforcement in the U.S., the U.K., and France
Key Points
- The use of ” race ” as a broad, non-scientific description of general appearance is a common practice in law enforcement agencies around the world.
- Racial profiling refers to the use of an individual’s race or ethnicity by law enforcement personnel as a key factor in determining whether to engage in enforcement (e.g., make a traffic stop or arrest). The practice is controversial and is illegal in some nations.
- In an attempt to facilitate the job of law enforcement officers, the FBI employs the term “race” to summarize the general appearance of individuals whom they are attempting to apprehend.
Key Terms
- racial profiling : Racial profiling refers to the use of an individual’s race or ethnicity by law enforcement personnel as a key factor in deciding whether to engage in enforcement (e.g., make a traffic stop or arrest).
Legal Definition of Race
Many governments provide legal definitions of race for purposes of census-taking and calculating budgets for governmental programs such as those that promote equal opportunity employment. For instance, in the U.S. Federal Office of Management and Budget (OMB) and the U.S. Census Bureau currently uses race and ethnicity as self-identification data items. In this system, the residents choose the race or races with which they most closely identify and indicate what their ethnic origin is (e.g., Latino).
The racial categories represent a social-political construct for the race or races that respondents consider themselves to be. OMB defines the concept of race as outlined for the U.S. census as not “scientific or anthropological” and takes into account “social and cultural characteristics as well as ancestry”, using “appropriate scientific methodologies” that are not “primarily biological or genetic in reference. ” The race categories include both racial and national-origin groups.
Race and Law Enforcement
In an attempt to provide general descriptions that may facilitate the job of law enforcement officers seeking to apprehend suspects, the FBI employs the term “race” to summarize the general appearance (skin color, hair texture, eye shape, and other such easily noticed characteristics) of individuals whom they are attempting to apprehend. From the perspective of law enforcement officers, it is generally more important to arrive at a description that will readily suggest the general appearance of an individual than to make a scientifically valid categorization by DNA or other such means. Thus, in addition to assigning a wanted individual to a racial category, such a description will include: height, weight, eye color, scars, and other distinguishing characteristics.
British Police use a classification based on the ethnic background of British society, for example W1 (White-British), M1 (White and black Caribbean), and A1 (Asian-Indian). Some of the characteristics that constitute these groupings are biological and some are learned (cultural or linguistic) traits that are easy to notice.
In many countries, such as France, the state is legally banned from maintaining data based on race, so the police issue wanted notices to the public that include labels like “dark skin complexion. ”
Racial Profiling
Racial profiling refers to the use of an individual’s race or ethnicity by law enforcement personnel as a key factor in deciding whether to engage in enforcement (e.g. make a traffic stop or arrest). The practice is controversial and is illegal in some nations.
In the United States, the practice of racial profiling has been ruled to be both unconstitutional and a violation of civil rights. There is active debate regarding the cause of a marked correlation between the recorded crimes, punishments meted out, and the country’s populations. Many consider de facto racial profiling an example of institutional racism in law enforcement. The history of misuse of racial categories to impact adversely one or more groups and to offer protection and advantage to another has a clear impact on the larger debate. This debate is concerned with the legitimacy of the government using known phenotypical or genotypical characteristics tied to the presumed race of both victims and perpetrators.


Discovering Sub-atomic Particles
Skills to Develop
- Describe the three types of radioactivity
- Understand the difference between atoms. ions, and isotopes
- Define the subatomic particles that make up atoms
At the end of the last section ( Valence ), we mentioned the problem of the masses of iodine and tellurium, which were "out of order" in the periodic table. This was only one of several problems facing chemists at this point. Another was the rare earth elements (the lanthanoides and actinoides, at the bottom of the periodic table). The rare earth elements were extremely similar to each other, so it was very hard to separate them, determine the masses, and fit them into the periodic table.
Another problem was ions . Ions were charged chemical entities that moved through solutions carrying electric current when electricity was applied. Chemists knew they existed, but could not explain how they formed. Cations were positively charged, while anions were negatively charged. Hydrogen was known to form positive ions with a particular charge. But where did the charges come from? Berzelius had thought that the atoms themselves were charged, but this didn't make sense after Avogadro's hypothesis was accepted, since in that case the two O atoms in O 2 would repel each other, not form a molecule. Of course, this was mostly a problem to physical chemists, because physicists mostly still didn't believe in atoms.
Experiments by Davy, Faraday and others showed that solids usually conduct electricity without changing themselves; liquids are decomposed by electrical current, and gases conduct badly and only at high voltage, but become better conductors at low pressure. Glass tubes of low pressure gas glow; examples include neon lights in store windows, fluorescent light bulbs, and yellow sodium lamps sometimes used at street lights. When glass tubes full of very low pressure gas were made by expert glassblower Geissler after 1850, a glowing spot would appear somewhere on the glass when the tube was connected to a high voltage. This spot could be moved by a magnet, suggesting that it was negatively charged. A beam or ray was coming out of the cathode (the electrode to which cations move), and this beam caused the glass to glow. (This is exactly how old TVs work, from before there were flat screens.)
But what was the beam that came out of the cathode? Some thought it was negatively-charged particles, while others (especially physicists) thought it was a wave. Thomson convinced himself that the beam is a negatively charged particle, which can be moved using electric or magnetic fields. He estimated that the particle has a charge/mass ratio 1000x greater than the hydrogen ion, but with the opposite charge. The ray that comes out of the cathode is the same whatever the material, and he found that you can generate the same particle by heating metal filaments very hot or exposing a metal surface to UV light (the light that gives you sunburns).
What are cathode rays? Electrons ! When Thomson suggested in 1897 that either they had a much higher charge or a much smaller mass than hydrogen ions, many people were skeptical. However, careful measurements by Millikan (starting 1908, continuing for almost 10 years!) of falling droplets of mist in an electric or magnetic field revealed that electrons have the same charge as hydrogen ions, but are almost ~1/2000 less massive, so in fact Thomson guessed electrons were twice as big as they really are.
In summary, electrons have an equal but opposite charge to hydrogen ions, but hydrogen ions weigh 2000x more than electrons. Electrons are part of every kind of atom.
Other than electrons, what are atoms made of? X-rays were discovered in 1895 when Roentgen noticed a ray that passed through the glass of his cathode ray tube and developed photographic film placed in its path, even if it was wrapped in dark paper. Inspired by this discovery, Becquerel studied the fluorescence (this means glowing after being exposed to light) of minerals and whether this could develop film through dark paper. He used sunlight to make the minerals fluoresce, but discovered that some minerals fluoresce even without sunlight. Minerals that contain the elements uranium and thorium have this property, which is called radioactivity . Three types of radioactivity were discovered, α (positive charge), β (electrons, same as cathode rays) and γ (light, similar to x-rays). This radiation is a property of the element, and is not changed by chemical combinations. It was also discovered that radioactive elements decay into products that closely resemble known elements, except that the masses are different. These decay products have exactly the same chemical properties as the known elements, and once mixed together, they can't be separated by chemical means. But the masses were different. The evidence against Dalton's "identical and indivisible atoms of each element" was getting strong.
Rutherford studied the α-radiation, and found that it had a positive charge, and an e/m (charge/mass) ratio 1/2 that of a hydrogen ion. Later he proved that it is a charged form of the element helium (He).
Finally, using an early version of the mass spectrometer, which measures e/m by accelerating charged particles in an electric or magnetic field, Aston determined that neon (Ne) atoms have masses of 20 or 22, not 20.2, then the accepted value. Here's another case where knowing the precision of your experiment is important: if he couldn't tell the difference between 20.0 and 20.2, this wouldn't have been useful! The two versions of Ne are called isotopes . Isotopes are atoms of the same element with have the same chemical properties, but have different masses.
What is the structure of an atom? At this point, it was clear that Dalton had not been entirely correct, because atoms of one element could exist in different forms, or isotopes. It was also becoming clear that atoms could be divided into smaller parts, like electrons. But how were the electrons and the positive parts (like the part of He that is α-radiation) arranged, and what was the positive particle? It seemed like there was a lot of empty space in atoms, because cathode rays could pass through aluminum windows. Many theories were considered, but ultimately two of Rutherford's students, Geiger and Marsden, found an answer. They observed that α-rays directed at a thin gold (Au) foil usually passed through the foil (though not usually quite straight), but sometimes the foil knocked them back in the direction they came from. These α-particles must have bumped into (or been repelled by a large positive charge in) something very heavy, to have so large a change in direction. In 1911, Rutherford proposed that atoms consist of a small dense particle, the nucleus , which contains most of the atom's mass and all of its positive charge, with electrons moving through a large empty space around the nucleus. But they were a little confused about the mass and charge of the nucleus.
In 1913, a very young chemist named Henry Moseley measured the fluorescence wavelength produced when x-rays shine on pure elemental samples. He discovered that if you graph the square root of the fluorescence frequency vs the element's location in the periodic table (such as H, 1; C, 6; Hg, 80) you get a straight line. The location in the periodic table is called atomic number . This confirmed the ordering of Te/I in the periodic table and a few other similar problems. He was also able to determine where undiscovered elements were missing in the table, and clarify identification of rare earth elements, which was very difficult because they were so similar. He was 26 years old, and he died a year later in WWI. Moseley's work showed that the ordering of the periodic table is based on the atomic number, which is the number of positive charges in the nucleus and also the number of electrons. The unit of positive charge is a hydrogen nucleus, or proton .
The mass of the nucleus continued to be confusing even after the amount of positive charge had been determined by Moseley's atomic numbers. The atomic weights were about double what they should be if the nucleus held only protons. A proposal to explain this was that there were some electrons in the nucleus, canceling out the charge of half the protons. Later radiochemistry experiments showed the existence of the neutron , which has about the mass of a proton and no charge. This was understood to be the extra mass in nuclei. Now, though, we know that neutrons can decay into protons and electrons (and some other less familiar particles), so the earlier idea wasn't far off.
Summary
Atoms are composed of protons, neutrons, and electrons. Protons and neutrons make most of the atom's mass and all of its positive charge in the nucleus . Protons are subatomic particles that contain a positive charge. Essentially, they are hydrogen nuclei. Neutrons are subatomic particles that have the same mass as a proton but not charge. Electrons are subatomic particles with a negative charge that are found outside of the atom's nucleus. An element's atomic number provides its location on the periodic table as well as describe how many protons are in an atoms of that particular element. Ions are atoms that are either positively or negatively charged due to the number of protons or electrons in an atom not being equal to each other. Isotopes are atoms that have a different number of neutrons in the nucleus than normal. There are three main types of radioactivity : α , β, and γ. α (Alpha) radiation involves the emission of a helium nucleus, which is two protons and two neutrons. β (Beta) radiation involves the emission of an electron from the atom's nucleus. γ (Gamma) radiation involves the emission of high-energy electromagnetic radiation.


9.7: Notations for Tensors
Learning Objectives
- Review notations
- Introduce new notations
Johnny is an American grade-school kid who has had his tender mind protected from certain historical realities, such as the political status of slaves, women, and Native Americans in the early United States. If Johnny ever tries to read the U.S. Constitution, he will be very confused by certain passages, such as the infamous three-fifths clause referring opaquely to “all other persons.”
This optional section is meant to expose you to some similar historical ugliness involving tensor notation, knowledge of which may be helpful if you learn general relativity in the future. As in the evolution of the U.S. Constitution and its interpretation, we will find that not all the changes have been improvements. In this section we brieﬂy recapitulate some notations that have already been introduced, and also introduce two new ones.
Concrete index notation
A displacement vector is our prototypical example of a tensor, and the original nineteenth-century approach was to associate this tensor with the changes in the coordinates. Tensors achieve their full importance in differential geometry, where space (or spacetime, in general relativity) may be curved, in the sense defined in section 2.2. In this context, only infinitesimally small displacements qualify as vectors; to see this, imagine displacements on a sphere, which do not commute for the reasons described in section 8.3. On small scales, the sphere’s curvature is not apparent, which is why we need to make our displacements infinitesimal. Thus in this approach, the simplest example of a relativistic tensor occurs if we pick Minkowski coordinates to describe a region of spacetime that is small enough for the curvature to be negligible, and we associate a displacement vector with a \(4\)-tuple of infinitesimal changes in the coordinates:
\[(dt,dx,dy,dz)\]
Until about 1960, this carried the taint of the lack of rigor believed to be associated with Leibniz-style infinitesimal numbers, but this difficulty was resolved and is no longer an argument against the notation. 1
Coordinate-independent notation
A more valid reason for disliking the old-school notation is that, as described in chapter 7, it is desirable to avoid writing every line of mathematics in a notation that explicitly refers to a choice of coordinates. We might therefore prefer, as Penrose began advocating around 1970, to notate this vector in coordinate-independent notation such as “birdtracks” (section 6.1),
\[\rightarrow dx\]
or the synonymous abstract index notation (section ??, p. ??),
\[dx^a\]
where the use of the Latin letter a means that we’re not referring to any coordinate system, a doesn’t take on values such as \(1\) or \(2\), and \(dx^a\) refers to the entire object \( \ rightarrow dx\), not to some real number or set of real numbers.
Unfortunately for the struggling student of relativity, there are at least two more notations now in use, both of them incompatible in various ways with the ones we’ve encountered so far.
Cartan notation
Our notation involving upper and lower indices is descended from a similar-looking one invented in 1853 by Sylvester. 2 In this system, vectors are thought of as invariant quantities. We write a vector in terms of a basis \({e_µ}\) as \(x = \sum x^\mu e_\mu\). Since \(x\) is considered invariant, it follows that the components \(x^µ\) and the basis vectors \(e_µ\) must transform in opposite ways. For example, if we convert from meters to centimeters, the \(x^µ\) get a hundred times bigger, which is compensated for by a corresponding shrinking of the basis vectors by \(1/100\).
This notation clashes with normal index notation in certain ways. One gotcha is that we can’t infer the rank of an expression by counting indices. For example, \(x = \sum x^\mu e_\mu\) is notated as if it were a scalar, but this is actually a notation for a vector.
Circa 1930, Élie Cartan augmented this notation with a trick that is perhaps a little too cute for its own good. He noted that the partial differentiation operators \(∂/∂x^µ\) could be used as a basis for a vector space whose structure is the same as the space of ordinary vectors. In the modern context we rewrite the operator \(∂/∂x^µ\) as \(∂_µ\) and use the Einstein summation convention, so that in the Cartan notation we express a vector in terms of its components as
\[x = x^\mu \partial _\mu\]
In the Cartan notation, the symbol dxµ is hijacked in order to represent something completely different than it normally does; it’s taken to mean the dual vector corresponding to \(∂_µ\). The set \({dx^µ}\) is used as a basis for notating covectors.
A further problem with the Cartan notation arises when we try to use it for dimensional analysis (see below).
Index-free notation
Independently of Penrose and the physics community, mathematicians invented a different coordinate-free notation, one without indices. In this notation, for example, we would notate the magnitude of a vector not as \(v_a v^b\) or \(g_{ab} v^a v^b\) but as
\[g(v,v)\]
This notation is too clumsy for use in complicated expressions involving tensors with many indices. As shown in the next section, it is also not compatible with the way physicists are accustomed to doing dimensional analysis.
Incompatibility of Cartan and index-free notation with dimensional analysis
In
section 9.6 we developed a system of dimensional analysis for use with abstract index notation. Here we discuss the issues that arise when we attempt to mix in other notational systems.One of the hallmarks of index-free notation is that it uses nonmultiplicative notation for many tensor products that would have been written as multiplication in index notation, e.g., \(g(v,v)\) rather than \(v^a v_a\). This makes the system clumsy to use for dimensional analysis, since we are accustomed to reasoning about units based on the assumption that the units of any term in an equation equal the product of the units of its factors.
In Cartan notation we have the problem that certain notations, such as \(dx^µ\), are completely redefined. The remainder of this section is devoted to exploring what goes wrong when we attempt to extend the analysis of section 9.6 to include Cartan notation. Let vector \(r\) and covector \(ω\) be duals of each other, and let \(r\) represent a displacement. In Cartan notation, we write these vectors in terms of their components, in some coordinate system, as follows:
\[r = r^µ∂_µ\]
\[ω = ω_µdx^µ\]
Suppose that the coordinates are Minkowski. Reading from left to right and from top to bottom, there are six quantities occurring in these equations. We attribute to them the units \(L^A, L^B, ...L^F\). If we follow the rule that multiplicative notation is to imply multiplication of units, then
\[A = B + C\]
and
\[D = E + F\]
For compatibility with the system in
section 9.6, equations 9.7.6 and 9.7.7 require\[A + D = 2σ\]
and
\[D = 2γ + B\]
To avoid a clash between Cartan and concrete index notation in a Minkowski coordinate system, it would appear that we want the following three additional conditions.
\[F = ξ \text { units of Cartan } dx^µ \text { not to clash with units of } dx^µ\]
\[C = -ξ \text { units of Cartan } ∂µ \text { not to clash with units of the derivative}\]
\[B = ξ \text { units of components in Cartan notation not to clash with units of } dx^µ\]
We have \(6\) unknowns and \(7\) constraints, so in general Cartan notation cannot be incorporated into this system without some constraint on the exponents \((σ,γ,ξ)\). In particular, we require \(ξ = 0\), which is not a choice that most physicists prefer.


3.4: Practices to Promote a Multicultural Classroom
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Curriculum and activities need to be carefully designed and implemented in the program. An antibias curriculum can help children to learn about their own identity and to respect different gender, ethnicity, races, backgrounds among people.
Teaching to Children’s various Learning Styles
Every child learns in different ways. To be able to meet children’s physical, emotional, social, and academic needs, educators need to know each child’s unique learning style.
Welcoming Family and Community Involvement
Educators should provide families and the community frequent opportunities to be involved in school activities. Some recommendations are personalizing your approach to the family, ensuring communication is nonjudgmental, expressing resolve in maintaining involvement, providing strong leadership and administrative support, and managing community outreach.
Supporting and Valuing Every Child
The concepts of valuing the individual and respect for human diversity have evolved slowly over the ages. Every child needs to be treated as an individual and children need to learn their own identity and background. [71]
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Supporting Children’s Understanding of Fairness and Respect for Others |
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“That’s not fair!” expresses a preschooler’s concern for fairness, and the child’s growing sensitivity to others’ feelings also contributes to this concern. Efforts to act fairly can be manifested in turn-taking, sharing, cooperation, and understanding how preschool program rules help to maintain fairness. During the preschool years, children gradually become more capable of balancing their own interests with those of other children and of respecting others’ desires and goals. Teachers contribute to these achievements as they explain rules (and the reasons for them) that emphasize fair conduct, the need to cooperate with the interests of others, and using words to help children understand another’s emotions, viewpoints, and goals. It is also important to assist children when they think that fair equals the same. Sometimes what is fair is doing what is needed for each child. There are times that a child may need an adult’s help to do something (e.g., hold the jar steady) and another child is asked to do it without an adult’s help. You can support this with the following interactions and strategies:
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7.5: What Are Intelligence and Creativity?
Learning Objectives
- Define intelligence
- Explain the triarchic theory of intelligence
- Identify the difference between intelligence theories
- Explain emotional intelligence
A four-and-a-half-year-old boy sits at the kitchen table with his father, who is reading a new story aloud to him. He turns the page to continue reading, but before he can begin, the boy says, “Wait, Daddy!” He points to the words on the new page and reads aloud, “Go, Pig! Go!” The father stops and looks at his son. “Can you read that?” he asks. “Yes, Daddy!” And he points to the words and reads again, “Go, Pig! Go!”
This father was not actively teaching his son to read, even though the child constantly asked questions about letters, words, and symbols that they saw everywhere: in the car, in the store, on the television. The dad wondered about what else his son might understand and decided to try an experiment.  He put the list down in front of the boy and asked him to read the words. “Mom, dad, dog, bird, bed, truck, car, tree,” he read, slowing down to carefully pronounce bird and truck. Then, “Did I do it, Daddy?” “You sure did! That is very good.” The father gave his little boy a warm hug and continued reading the story about the pig, all the while wondering if his son’s abilities were an indication of exceptional intelligence or simply a normal pattern of linguistic development. Like the father in this example, psychologists have wondered what constitutes intelligence and how it can be measured.
Classifying Intelligence
What exactly is intelligence? The way that researchers have defined the concept of intelligence has been modified many times since the birth of psychology. British psychologist Charles Spearman believed intelligence consisted of one general factor, called \(g\) , which could be measured and compared among individuals. Spearman focused on the commonalities among various intellectual abilities and demphasized what made each unique. Long before modern psychology developed, however, ancient philosophers, such as Aristotle, held a similar view (Cianciolo & Sternberg, 2004).
Others psychologists believe that instead of a single factor, intelligence is a collection of distinct abilities. In the 1940s, Raymond Cattell proposed a theory of intelligence that divided general intelligence into two components: crystallized intelligence and fluid intelligence (Cattell, 1963). Crystallized intelligence is characterized as acquired knowledge and the ability to retrieve it. When you learn, remember, and recall information, you are using crystallized intelligence. You use crystallized intelligence all the time in your coursework by demonstrating that you have mastered the information covered in the course. Fluid intelligence encompasses the ability to see complex relationships and solve problems. Navigating your way home after being detoured onto an unfamiliar route because of road construction would draw upon your fluid intelligence.
Other theorists and psychologists believe that intelligence should be defined in more practical terms. For example, what types of behaviors help you get ahead in life? Which skills promote success? Think about this for a moment. Being able to recite all \(44\) presidents of the United States in order is an excellent party trick, but will knowing this make you a better person?
Robert Sternberg developed another theory of intelligence, which he titled the triarchic theory of intelligence because it sees intelligence as comprised of three parts (Sternberg, 1988): practical, creative, and analytical intelligence.
Practical intelligence , as proposed by Sternberg, is sometimes compared to “street smarts.” Being practical means you find solutions that work in your everyday life by applying knowledge based on your experiences. This type of intelligence appears to be separate from traditional understanding of IQ; individuals who score high in practical intelligence may or may not have comparable scores in creative and analytical intelligence (Sternberg, 1988).
This story about the 2007 Virginia Tech shootings illustrates both high and low practical intelligences. During the incident, one student left her class to go get a soda in an adjacent building. She planned to return to class, but when she returned to her building after getting her soda, she saw that the door she used to leave was now chained shut from the inside. Instead of thinking about why there was a chain around the door handles, she went to her class’s window and crawled back into the room. She thus potentially exposed herself to the gunman. Thankfully, she was not shot. On the other hand, a pair of students was walking on campus when they heard gunshots nearby. One friend said, “Let’s go check it out and see what is going on.” The other student said, “No way, we need to run away from the gunshots.” They did just that. As a result, both avoided harm. The student who crawled through the window demonstrated some creative intelligence but did not use common sense. She would have low practical intelligence. The student who encouraged his friend to run away from the sound of gunshots would have much higher practical intelligence.
Analytical intelligence is closely aligned with academic problem solving and computations. Sternberg says that analytical intelligence is demonstrated by an ability to analyze, evaluate, judge, compare, and contrast. When reading a classic novel for literature class, for example, it is usually necessary to compare the motives of the main characters of the book or analyze the historical context of the story. In a science course such as anatomy, you must study the processes by which the body uses various minerals in different human systems. In developing an understanding of this topic, you are using analytical intelligence. When solving a challenging math problem, you would apply analytical intelligence to analyze different aspects of the problem and then solve it section by section.
Creative intelligence is marked by inventing or imagining a solution to a problem or situation. Creativity in this realm can include finding a novel solution to an unexpected problem or producing a beautiful work of art or a well-developed short story. Imagine for a moment that you are camping in the woods with some friends and realize that you’ve forgotten your camp coffee pot. The person in your group who figures out a way to successfully brew coffee for everyone would be credited as having higher creative intelligence.
Multiple Intelligences Theory was developed by Howard Gardner, a Harvard psychologist and former student of Erik Erikson. Gardner’s theory, which has been refined for more than \(30\) years, is a more recent development among theories of intelligence. In Gardner’s theory, each person possesses at least eight intelligences. Among these eight intelligences, a person typically excels in some and falters in others (Gardner, 1983). The Table below describes each type of intelligence.
| Intelligence Type | Characteristics | Representative Career |
|---|---|---|
| Linguistic intelligence | Perceives different functions of language, different sounds and meanings of words, may easily learn multiple languages | Journalist, novelist, poet, teacher |
| Logical-mathematical intelligence | Capable of seeing numerical patterns, strong ability to use reason and logic | Scientist, mathematician |
| Musical intelligence | Understands and appreciates rhythm, pitch, and tone; may play multiple instruments or perform as a vocalist | Composer, performer |
| Bodily kinesthetic intelligence | High ability to control the movements of the body and use the body to perform various physical tasks | Dancer, athlete, athletic coach, yoga instructor |
| Spatial intelligence | Ability to perceive the relationship between objects and how they move in space | Choreographer, sculptor, architect, aviator, sailor |
| Interpersonal intelligence | Ability to understand and be sensitive to the various emotional states of others | Counselor, social worker, salesperson |
| Intrapersonal intelligence | Ability to access personal feelings and motivations, and use them to direct behavior and reach personal goals | Key component of personal success over time |
| Naturalist intelligence | High capacity to appreciate the natural world and interact with the species within it | Biologist, ecologist, environmentalist |
Gardner’s theory is relatively new and needs additional research to better establish empirical support. At the same time, his ideas challenge the traditional idea of intelligence to include a wider variety of abilities, although it has been suggested that Gardner simply relabeled what other theorists called “cognitive styles” as “intelligences” (Morgan, 1996). Furthermore, developing traditional measures of Gardner’s intelligences is extremely difficult (Furnham, 2009; Gardner & Moran, 2006; Klein, 1997).
Gardner’s inter- and intrapersonal intelligences are often combined into a single type: emotional intelligence. Emotional intelligence encompasses the ability to understand the emotions of yourself and others, show empathy, understand social relationships and cues, and regulate your own emotions and respond in culturally appropriate ways (Parker, Saklofske, & Stough, 2009). People with high emotional intelligence typically have well-developed social skills. Some researchers, including Daniel Goleman, the author of Emotional Intelligence: Why It Can Matter More than IQ , argue that emotional intelligence is a better predictor of success than traditional intelligence (Goleman, 1995). However, emotional intelligence has been widely debated, with researchers pointing out inconsistencies in how it is defined and described, as well as questioning results of studies on a subject that is difficulty to measure and study emperically (Locke, 2005; Mayer, Salovey, & Caruso, 2004)
Intelligence can also have different meanings and values in different cultures. If you live on a small island, where most people get their food by fishing from boats, it would be important to know how to fish and how to repair a boat. If you were an exceptional angler, your peers would probably consider you intelligent. If you were also skilled at repairing boats, your intelligence might be known across the whole island. Think about your own family’s culture. What values are important for Latino families? Italian families? In Irish families, hospitality and telling an entertaining story are marks of the culture. If you are a skilled storyteller, other members of Irish culture are likely to consider you intelligent.
Some cultures place a high value on working together as a collective. In these cultures, the importance of the group supersedes the importance of individual achievement. When you visit such a culture, how well you relate to the values of that culture exemplifies your cultural intelligence , sometimes referred to as cultural competence.
Creativity
Creativity is the ability to generate, create, or discover new ideas, solutions, and possibilities. Very creative people often have intense knowledge about something, work on it for years, look at novel solutions, seek out the advice and help of other experts, and take risks. Although creativity is often associated with the arts, it is actually a vital form of intelligence that drives people in many disciplines to discover something new. Creativity can be found in every area of life, from the way you decorate your residence to a new way of understanding how a cell works.
Creativity is often assessed as a function of one’s ability to engage in divergent thinking . Divergent thinking can be described as thinking “outside the box;” it allows an individual to arrive at unique, multiple solutions to a given problem. In contrast, convergent thinking describes the ability to provide a correct or well-established answer or solution to a problem (Cropley, 2006; Gilford, 1967).
EVERYDAY CONNECTION: Creativity
Dr. Tom Steitz, the Sterling Professor of Biochemistry and Biophysics at Yale University, has spent his career looking at the structure and specific aspects of RNA molecules and how their interactions cold help produce antibiotics and ward off diseases. As a result of his lifetime of work, he won the Nobel Prize in Chemistry in 2009. He wrote, “Looking back over the development and progress of my career in science, I am reminded how vitally important good mentorship is in the early stages of one's career development and constant face-to-face conversations, debate and discussions with colleagues at all stages of research. Outstanding discoveries, insights and developments do not happen in a vacuum” (Steitz, 2010, para. 39). Based on Steitz’s comment, it becomes clear that someone’s creativity, although an individual strength, benefits from interactions with others. Think of a time when your creativity was sparked by a conversation with a friend or classmate. How did that person influence you and what problem did you solve using creativity?
Summary
Intelligence is a complex characteristic of cognition. Many theories have been developed to explain what intelligence is and how it works. Sternberg generated his triarchic theory of intelligence, whereas Gardner posits that intelligence is comprised of many factors. Still others focus on the importance of emotional intelligence. Finally, creativity seems to be a facet of intelligence, but it is extremely difficult to measure objectively.
Glossary
- analytical intelligence
- aligned with academic problem solving and computations
- convergent thinking
- providing correct or established answers to problems
- creative intelligence
- ability to produce new products, ideas, or inventing a new, novel solution to a problem
- creativity
- ability to generate, create, or discover new ideas, solutions, and possibilities
- crystallized intelligence
- characterized by acquired knowledge and the ability to retrieve it
- cultural intelligence
- ability with which people can understand and relate to those in another culture
- divergent thinking
- ability to think “outside the box” to arrive at novel solutions to a problem
- emotional intelligence
- ability to understand emotions and motivations in yourself and others
- fluid intelligence
- ability to see complex relationships and solve problems
- Multiple Intelligences Theory
- Gardner’s theory that each person possesses at least eight types of intelligence
- practical intelligence
- aka “street smarts”
- triarchic theory of intelligence
- Sternberg’s theory of intelligence; three facets of intelligence: practical, creative, and analytical
Contributors and Attributions
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Rose M. Spielman with many significant contributors. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the creative commons license and may not be reproduced without the prior and express written consent of Rice University. For questions regarding this license, please contact<EMAIL_ADDRESS>.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>.


2.3.5: Responsibilities to Stakeholders
How Do Businesses Meet Their Social Responsibilities to Various Stakeholders?
What makes a company be admired or perceived as socially responsible? Such a company meets its obligations to its stakeholders. Stakeholders are the individuals or groups to whom a business has a responsibility. The stakeholders of a business are its employees, its customers, the general public, and its investors.
Responsibility to Employees
An organization’s first responsibility is to provide a job to employees. Keeping people employed and letting them have time to enjoy the fruits of their labor is the finest thing business can do for society. Beyond this fundamental responsibility, employers must provide a clean, safe working environment that is free from all forms of discrimination. Companies should also strive to provide job security whenever possible.
Enlightened firms are also empowering employees to make decisions on their own and suggest solutions to company problems. Empowerment contributes to an employee’s self-worth, which, in turn, increases productivity and reduces absenteeism.
Each year, in collaboration with Great Place to Work ® , Fortune conducts an extensive employee survey of the best places to work in the United States. For 2017, the top companies included Google, Wegmans Food Markets, Edward Jones, Genentech, Salesforce, Acuity, and Quicken Loans. Some companies offer unusual benefits to their employees. For example, biotech company Genentech offers employee compensation for taking alternative methods of transportation to work at its South San Francisco campus. Employees can earn $12 per day for walking or biking to work, and those who drive a carpool or vanpool can earn $8 and $16, respectively. In addition, the company offers free commuter bus service for all employees via 27 routes around the Bay Area.
Responsibility to Customers
To be successful in today’s business environment, a company must satisfy its customers. A firm must deliver what it promises, as well as be honest and forthright in everyday interactions with customers, suppliers, and others. Recent research suggests that many consumers, particularly millennials, prefer to do business with companies and brands that communicate socially responsible messages, utilize sustainable manufacturing processes, and practice ethical business standards.
Responsibility to Society
A business must also be responsible to society. A business provides a community with jobs, goods, and services. It also pays taxes that go to support schools, hospitals, and better roads. Some companies have taken an additional step to demonstrate their commitment to stakeholders and society as a whole by becoming Certified Benefit Corporations, or B Corps for short. Verified by B Lab, a global nonprofit organization, B Corps meet the highest standards of social and environmental performance, public transparency, and legal accountability and strive to use the power of business to solve social and environmental problems via an impact assessment that rates each company on a possible score of 200 points. To become certified as a Benefit Corporation, companies need to reach a score of at least 80 and must be recertified every two years. There are more than 2,000 companies worldwide that have been certified as B Corps, including Method, W.S. Badger Company, Fishpeople Seafood, LEAP Organics, New Belgium Brewing Company, Ben & Jerry’s, Cabot Creamery Co-op, Comet Skateboards, Etsy, Patagonia, Plum Organics, and Warby Parker.
Environmental Protection
Business is also responsible for protecting and improving the world’s fragile environment. The world’s forests are being destroyed fast. Every second, an area the size of a football field is laid bare. Plant and animal species are becoming extinct at the rate of 17 per hour. A continent-size hole is opening up in the earth’s protective ozone shield. Each year we throw out 80 percent more refuse than we did in 1960; as a result, more than half of the nation’s landfills are filled to capacity.
To slow the erosion of the world’s natural resources, many companies have become more environmentally responsible. For example, Toyota now uses renewable energy sources such as solar, wind, geothermal, and water power for electricity to run its facilities. When its new $1 billion North American headquarters opened in Plano, Texas, in May 2017, Toyota said the 2.1 million-square-foot campus would eventually be powered by 100% clean energy, helping the auto giant move closer to its goal of eliminating carbon emissions in all of its operations.
ETHICS IN PRACTICE
This Fish Story Has a Tasting Ending
Duncan Berry has always been an environmentalist at heart. Brought up on the Oregon coast, he was a sea captain at an early age, spending nearly two decades on the ocean before going on to become a successful entrepreneur in the organic cotton industry. After selling the textile business at the age of 50, he retired back to the Oregon coast to work on a state initiative to preserve marine habitats.
He quickly discovered that the state’s commercial fishing industry had gone into major disrepair since his seafaring adventure years earlier. Berry learned the majority of seafood consumed in the United States was being imported from other countries and more than 90 percent of U.S. seafood was being exported. In addition, great harm was being done to the ocean because it was being overfished.
Although several groups were already working to improve the commercial fishing industry, he observed that one key group was not part of the discussion: consumers. Berry decided a key component of change had to be involving consumers in the process. He spent more than a year meeting with everyone involved in the Oregon fishing industry—from fishermen to processors, distributors, truck drivers, chefs, and consumers—to gain perspective on why the industry was failing. His “aha” moment occurred when he realized the majority of fish is consumed in restaurants because consumers think preparing fish at home is too difficult and time-consuming. That’s when he co-founded Fishpeople Seafood.
Started in 2012, Fishpeople has a mission of changing the way people think about seafood by being transparent about where the seafood comes from, how it is processed, and how it is handled. Berry believes the company’s transparency helps consumers understand how the process translates into sustainable food that tastes good and is good for you. The company makes shelf-stable, ready-to-eat restaurant-quality seafood in the form of soups, meal kits, and fresh and frozen filets, complete with farm-to-table ingredients. On every package there is a code consumers can enter at the company’s website that will tell them everything about the seafood’s origin, down to the fisherman who caught it. Fishpeople also operates a processing plant in Toledo, Oregon, where workers are paid a livable wage and receive health insurance—benefits typically unheard of in the fishing industry.
Fishpeople’s products are available in more than 5,000 stores nationwide, including Walmart, Whole Foods, Costco, Kroger, and other grocery stores and markets. Recently the company announced a merger with Ilwaco Landing Fishermen, which will help further the two groups’ shared vision of supporting local fishermen and providing sustainable seafood to consumers.
Discussion Questions
- How does Fishpeople’s transparency contribute to the company’s success?
- What responsibility, if any, does Fishpeople have to the local fishing industry?
Corporate Philanthropy
Companies also display their social responsibility through corporate philanthropy. Corporate philanthropy includes cash contributions, donations of equipment and products, and support for the volunteer efforts of company employees. Recent statistics suggest U.S. corporate philanthropy exceeds more than $19 billion annually. American Express is a major supporter of the American Red Cross. The organization relies almost entirely on charitable gifts to carry out its programs and services, which include disaster relief, armed-forces emergency relief, blood and tissue services, and health and safety services. The funds provided by American Express have enabled the Red Cross to deliver humanitarian relief to victims of numerous disasters around the world. When Hurricane Katrina hit the Gulf Coast, Bayer sent 45,000 diabetes blood glucose monitors to the relief effort. Within weeks of the disaster, Abbott, Alcoa, Dell, Disney, Intel, UPS, Walgreens, Walmart, and others contributed more than $550 million for disaster relief.
Responsibilities to Investors
Companies’ relationships with investors also entail social responsibility. Although a company’s economic responsibility to make a profit might seem to be its main obligation to its shareholders, some investors increasingly are putting more emphasis on other aspects of social responsibility.
Some investors are limiting their investments to securities (e.g., stocks and bonds) that coincide with their beliefs about ethical and social responsibility. This is called social investing . For example, a social investment fund might eliminate from consideration the securities of all companies that make tobacco products or liquor, manufacture weapons, or have a history of being environmentally irresponsible. Not all social investment strategies are alike. Some ethical mutual funds will not invest in government securities because they help to fund the military; others freely buy government securities, with managers noting that federal funds also support the arts and pay for AIDS research. Today, assets invested using socially responsible strategies total more than $7 trillion.
Perhaps partly as the result of the global recession of 2007–2009, over the last several years companies have tried to meet responsibilities to their investors as well as to their other stakeholders. Recent research suggests that now more than ever, CEOs are being held to higher standards by boards of directors, investors, governments, media, and even employees when it comes to corporate accountability and ethical behavior. A recent global study by PwC reveals that over the last several years, there has been a large increase in the number of CEOs being forced out due to some sort of ethical lapse in their organizations. Strategies to prevent such missteps should include establishing a culture of integrity to prevent anyone from breaking the rules, making sure company goals and metrics do not create undue pressure on employees to cut corners, and implementing effective processes and controls to minimize the opportunity for unethical behavior.
CONCEPT CHECK
- How do businesses carry out their social responsibilities to consumers?
- What is corporate philanthropy?
- Is a company’s only responsibility to its investors to make a profit? Why or why not?


2.8: Medical Language Related to the Whole Body Learning Activities
Interactive Learning Activity: Practice labelling body cavities with this drag and drop activity.
Query \(\PageIndex{1}\)
Interactive Learning Activity: Practice labelling quadrants with this drag and drop activity.
Query \(\PageIndex{2}\)
Interactive Learning Activity: Practice labelling planes by dragging the name of the plane to its corresponding position.
Query \(\PageIndex{3}\)
Interactive Learning Activity: Study terms discussed in this chapter using these flashcards.
Query \(\PageIndex{4}\)
Interactive Learning Activity: Quiz yourself on terms related to the human body.
Query \(\PageIndex{5}\)
Interactive Learning Activity: Quiz yourself on terms related to the human body.
Query \(\PageIndex{6}\)
Interactive Learning Activity: Drag and drop terms describing body planes.
Query \(\PageIndex{7}\)
Interactive Learning Activity: Match opposite directional terms.
Query \(\PageIndex{8}\)
You can also print this as a Chapter 2 Practice Worksheet and check your answers with this Answer Key PDF .