3.1: Planning Happens in a Cycle
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- Jennifer Paris, Kristin Beeve, & Clint Springer
- College of the Canyons
To begin to understand how to plan effective, developmentally appropriate curriculum for children, we must look at the context in which that planning should happen. Planning everything, from the flow of the day, to how teachers design and stock the classroom environment, to the way the spontaneous (unplanned) experiences of children are recognized and valued, to the experiences teachers thoughtfully plan and intentionally implement, happens in a continuous cycle. As we will discuss in this chapter that cycle begins with observing and continues through documenting what was observed, reflecting on what it means and how to plan to best support children, and then implementing those plans, before returning back to observing. [1]
Planning curriculum for young children begins with teachers discovering, through careful listening and observation, each child’s development. Observation is an essential skill for a teacher. When teachers mindfully observe, they discover how individual children make meaning in everyday moments of play and interactions and how to deepen their relationships with children. Observing for the purpose of assessing individual children’s learning means carefully watching and listening, with thought and reflection. In doing so, teachers find the knowledge, awareness, and strategies that individual children have formed during their experiences. It may be evidence that pertains to individual children’s emotional, social, cognitive, or physical development. If the evidence is clear and significant, teachers can preserve it through, for example, a note, a photo, or a sample of a child’s work.
Consider this example in which teachers found various ways in which the children’s engagement in learning about snails related to the developmental profiles of different children:
As the children’s interest in the snails continued, the teachers looked for ways to expand learning opportunities and integrate them into the multifaceted experience. The teachers also reviewed individual children’s developmental profiles to be mindful of children’s developmental progress in different areas. In addition to the many counting opportunities in the environment, the teachers decided to integrate counting into the children’s exploration of snails. Younger children who were making progress with learning to count objects between five and ten were invited to set up a specific number (less than ten) of trays and snails.
Before the children started, the teachers reminded them of an earlier conversation about how to care for snails. In response, one of the children asked to show the others how to handle the snails gently. (Learning about counting was happening at the same time as learning about controlling the impulse to handle other creatures roughly instead of being gentle with them.) Teachers suggested to other children who were continuing to make progress with counting to count out a quantity of sticks, bark, or leaves greater than ten. Other children were asked to divide the snails evenly between the trays. The children kept saying to themselves, “Be gentle,” and handled the snails with great care.
As teachers observed each group, they helped children develop mathematical thinking by prompting them and asking questions. For example, at one table, a teacher noticed that children were counting some sticks twice. She said, “I wonder what would happen if we put each stick on the other side of the tray after counting it.” The children tried out this idea. Teachers noted children’s efforts and placed the notes, with the date recorded, into the children’s individual portfolios to be used as evidence for later reference when considering developmental progress relating to number sense and impulse control.
As teachers observe children’s play and interactions, they discover ways to support children’s learning. Ideas for the next steps in curriculum planning emerge as teachers reflect on how they might extend or expand children’s thinking, language, and interactions. Observation, reflection, and documentation in the moment simultaneously launch an ongoing assessment of each child’s progress in learning as well as the curriculum planning cycle. [3]
Here is a visual representation of the Curriculum Planning Cycle
Let’s explore each part of the cycle.
Observe
Observation means being present with children and attentive as they play and interact with others and the environment. This mindful kind of presence is different from participating in children’s play or directing their play. Whether for one minute or five, an attentive, mindful presence means waiting to see what unfolds in order to gain a complete picture of children’s play. A teacher who observes children as a first step in supporting learning discovers small scientists at work—experimenting, comparing, making assumptions, evaluating assumptions through their actions. Over time, children build mastery of a wide range of concepts and skills. The vignette about the snail exploration illustrates the role of the teacher as observer:
During small-group time with the snails, the teacher noticed a child who had been reluctant to hold a snail. This child had a visual impairment. As the teacher gently placed a snail on this child’s hand, two children watched and listened as the teacher commented, “He’s sticking his head out now, and he’s turned toward your fingers. Can you feel him crawling toward your fingers?” The other children who had been watching intently began to repeat the teacher’s encouraging words, saying, “He’s sticking his head out. He’s going toward your fingers!”
The teacher wrote down her observations and added an interpretive note that the children’s behavior may be a growing sign of empathy as measured by the DRDP, and the other child’s willingness to hold the snail, a growing sign of curiosity and initiative, also a DRDP measure. [5]
Observation Happens Through Lenses
It takes practice to become a good observer. An important aspect of being a good observer involves becoming aware of what is noticed and how observations are interpreted. Children may be influenced by many things. Culture, temperament, personal experiences, professional knowledge, and even community values and messages in the media affect how teachers see and experience children. These “lenses” through which teachers observe and interpret are at work even though they may not always be conscious of them. [6]
The Importance of Accuracy
Observations about children should be factual and objective to be useful and meaningful. Teachers should document only what they see and hear (the facts) and avoid using words that communicate judgment about a child’s feelings, intentions, and motivations; are ambiguous and open to interpretation; or describe an opinion. One way teachers may think about their own objectivity is to ask themselves: Am I describing this child’s behaviors and interactions in the same or a similar way that someone else observing this child would describe them?
Interpreting the meaning of children’s behaviors and interactions is important, and impressions, feelings, and insights about children are extremely valuable to the individualizing process. However, teachers first need accurate, factual information in order to draw conclusions later on about children’s skills, behavior, interests, and needs. [7]
Pause to Reflect
Think about yourself as an observer. What do you think will come most easily to you? What do you think will be more challenging?
Document
Documenting means gathering and holding evidence of children’s play and interests for future use. A common form of documentation in early childhood settings is a written note, often referred to as an observation anecdote. Anecdotal notes, along with other forms of documentation, in particular photos, video recordings, and work samples, serve a dual purpose. First, they preserve a teacher’s observations of children’s expressions of feelings, their thinking, and their learning. These documentations are guides to the next steps in day-to-day curriculum planning. And second, anecdotal notes and other evidence can be used to support a teacher’s periodic assessment of a child’s progress. An episode during the snail exploration highlights the dual purpose of documentation:
During their initial encounters with the snails, the children asked questions and made comments about the snail shells, the way the snails moved across the tray, and what the snails ate. Although several children were reluctant to pick up the snails, others were challenged by having to wait. The teachers recorded children’s distinct responses, writing down significant elements of what children said or did. For example, for a child with identified special needs related to self-regulation, a teacher noted: “Jasmine pushed aside Yuri in order to pick up the snail crawling off the tray. Yuri stumbled, fell, and began to cry. Jasmine continued to focus on the snail, saying nothing to Yuri.” For the teacher, Jasmine’s behavior was significant. This anecdotal note provided some evidence of Jasmine’s struggles with impulse control. It added to the growing evidence that Jasmine was still developing impulse control and empathy. Later, as the teacher shared her observation with her co-teacher and with Jasmine’s father in a conference, they discussed how the small group work around keeping the snails safe might support Jasmine as well as other children in reading cues of others and in thinking before acting in order to keep people safe. [9]
Documenting What is Observed
Teachers must be intentional about capturing and recording what children do and say by setting up a system for carrying out observations. There is no one right way to do this. Systems will look different from program to program, and even classroom to classroom. Additionally, observation systems are not static; they should be revisited as teachers become more proficient in observing children and as children grow and develop. However, there are some general strategies that should be considered when developing a system.
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Plan times to observe each child regularly and over time. This should include observing children
- Across settings (e.g., indoor and outdoor) and times of the day (morning, afternoon)
- During routines (e.g., mealtimes, naptime, arrival/departure, transitions)
- As they engage in spontaneous play experiences and planned activities and experiences
- As they interact with other children and adults.
- Plan for spontaneous observation opportunities, too.
- Have materials at hand to capture unexpected, but valuable observations of children.
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Decide how to organize and store observations with the system that works best for the individual teacher or teaching team. For example:
- A file folder for each child kept in hanging files in file cabinet, large box, or crate
- Index cards in file box with a section for each child
- A 3-ring binder notebook for each child
- An accordion folder for each child
- Hanging shoe bag, with pockets labeled for each child
- Decide how often to review observations. A system for using the valuable date from observations is an important part of the curriculum cycle. Some curriculum planning may be easy to implement based on just casual observation. But deeper analysis of observation of individual and groups of children will likely lend valuable insight in what teachers can plan to support optimal development.
- Include families in this process. Invite them to share what they observe about their children verbally, through pictures and photographs, or in writing. [11]
Portfolios
One way to document children’s development and learning are portfolios. Portfolios are collections of children’s work, notes and photographs from families, checklists and other print recording tools, and other items that document what children know and can do. Written observation notes, photos, and audio and video files may be included as part of the portfolio. Portfolios may be physical, virtual (some online assessment tools allow users to input observation notes and upload photos, video, and audio files for each child), or a combination of both.
To be useful, portfolio items should:
- Be dated and filed in order
- Represent various parts of the program (e.g., routines, play experiences, transitions)
- Present a balanced view of the child’s growth in all developmental domains.
Over time, the portfolio collection serves as a concrete record of the child’s progress toward individual goals as well as the program’s school readiness goals, so it should be reviewed regularly with families. Teachers should explain what they include in the portfolio and why they include it. They should also actively encourage families to contribute information and items to their child’s portfolio. [12]
Pause to Reflect
As you think about how to document children’s learning, what systems do you find most appealing? Which do you think would be most effective? Which are least appealing or do you think would be least effective?
Reflect & Plan
As teachers reflect on children’s play, they discover possibilities for designing curriculum to sustain, extend, and help children’s play to be more complex and, consequently, support the children’s continuing learning. [13]
Teachers ask themselves questions about what the information they have documented in observations of children says about the children’s development, interests, and needs. The answers to these questions lead to individualizing care and learning. There are many questions that teachers may ask themselves. For example:
- What developmental skill or activity does the child appear to be working on?
- What strategies does the child use to play with different toys?
- Does the child engage with objects or people differently than a month ago? What has changed? What has not changed?
- Do my actions/the actions of other adults who interact with the child affect the outcomes of the child’s experience? How so?
- How does the information relate to goals for the child? The family’s goals? The program’s school readiness goals?
- What other information do I need?
- What questions do I have for the child’s family?
It is during the reflective process that interpreting the meaning of children’s behaviors and interactions becomes important. These interpretations and insights give rise to each child’s story. Each child’s story informs responsive practice.
Teachers use what they know about each child to
- Adapt the environment
- Modify the daily schedule and/or routines
- Make decisions about how to guide the children’s learning based on what the child knows and can do as well as what the child is ready to try. [14]
That process of reflections then informs possible next steps in the curriculum. Possible steps might include adding materials to interest areas, books to read with large or small groups, activities to do in small groups, or a topic to investigate over time with the children. With clear ideas or objectives in mind, teachers plan curriculum that includes strategies to enhance the learning of all children in a group, as well as strategies to support the learning of individual children. Here is how reflection, discussion, and planning worked in the snail exploration:
While the children were exploring snails, teachers met each week to reflect and plan for the next steps in the children’s explorations. They decided to schedule time for small groups of children to explore the snails in a more focused way, hoping to extend the children’s learning and add complexity. The teachers planned a series of walks that would allow all the children to find snails in natural habitats. [15]
Pause to Reflect
Think back to something in your childhood that you were passionately interested or engaged in that someone observing you could have documented. What questions could your teachers have asked themselves about your experiences? How could they have planned?
(If it’s easier or more relevant, you can think of a child you know and consider what you can ask yourself and plan around what you know about that child.)
Implement
Once a plan is written, teachers implement it. While implementing a plan, teachers observe, reflect, and document. The curriculum-planning cycle begins again (or continues) as teachers watch to discover how children respond to the planned curriculum and how children show evidence of their development during the planned learning encounters. Teachers often approach this step with a sense of wonder, for they may be surprised and amazed by the children’s responses.
To hold the responses in memory, teachers may record notes, take a photo, or label, date, and keep a work sample, all of which they can later review to assess the impact of the curriculum plans. The evidence collected will help teachers to come up with ideas for supporting and assessing the children’s learning. Teachers might ponder the following questions:
- Are children responding as predicted, or were there surprises?
- What do the children’s responses tell us? How might we name the children’s interest(s) or intention(s)? What concepts and ideas are the children forming within their play?
- How might children who are English learners and children who speak English collaborate in small groups to learn from one another?
- Are children showing evidence of progress on any of the measures of the DRDP?
Here is what happened when the teachers implemented their idea of going on walks with the children to find snails in natural habitats:
Before going on their snail hunt, a small group of children gathered on a blanket with the teacher. Each child was provided with a clipboard with paper for taking “notes” while the teacher explained how the walk would be a way to find snails that lived outside their classroom. Some children pretended to write while the teacher talked, while others drew pictures of snails. In this group, teachers included two children who were fluent in Spanish and learning English. The teachers anticipated much conversation among children during the search for the snails and wanted to give these children a chance to converse in their home language as well as to share experiences with peers who spoke only English.
Before heading off on the hunt, the teacher suggested, “Let’s estimate. How many snails do you think we will find? Each of you can guess.” On a large sheet of paper that the children could easily see, she wrote each child’s name, saying each letter as she did so, and next to each name, the number guessed by that child.
Armed with magnifying glasses, the children went off to collect snails. There were many discoveries along the walk, not just snails. As children found snails, they carried them to a large examination tray set up on a table. Some children took a break from their snail search to examine, touch, and draw the snails already collected. At the end of the hunt, the children lined up the snails on a small log and counted them. The teacher suggested that they compare the number they counted with their estimates.
Before returning to their classroom, the children put the snails back into their natural habitats. The children were excited about sharing their experiences with other teachers and peers when they returned.
The teachers examined and reflected on what they saw in the children’s writings and drawings on the clipboards. They decided that some of the work samples were significant in showing how individual children were developing an idea, concept, or skill. They filed those samples in the children’s portfolios as evidence of developmental progress. [18]
Pause to Reflect
What happens when implementation goes differently than expected? What would have happened if the children had discovered and become fascinated with dandelions on their hunt for snails (and subsequently lost interest in the snails)? Does curriculum have to go as planned? Why or why not?
References
[1] Content by Jennifer Paris is licensed under CC BY 4.0
[2] Image by Noj Han is licensed under CC BY-SA 2.0
[3] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission (pg. 19-20)
[4] Image by Ian Joslin references image by the California Department of Education
[5] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission
[6] Observation: The Heart of Individualizing Responsive Care by the Office of Head Start is in the public domain
[7] Observation: The Heart of Individualizing Responsive Care by the Office of Head Start is in the public domain (pg. 9)
[8] Image by mintchipdesigns on Pixabay
[9] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission (pg. 21)
[10] Image by Airman 1st Class Kathryn R.C. Reaves is in the public domain
[11] Observation: The Heart of Individualizing Responsive Care by the Office of Head Start is in the public domain
[12] Observation: The Heart of Individualizing Responsive Care by the Office of Head Start is in the public domain
[13] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission
[14] Observation: The Heart of Individualizing Responsive Care by the Office of Head Start is in the public domain
[15] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission
[16] Image by Christina Morillo on Pexels
[17] Image by Jackie is licensed under CC BY 2.0
[18] California Preschool Curriculum Framework, Volume 1 by the California Department of Education is used with permission


21.6: Removing an Indwelling Urinary Catheter
It is the nurse’s responsibility to assess for a patient’s continued need for an indwelling catheter daily and to advocate for removal when appropriate. [1] Prolonged use of indwelling catheters increases the risk of developing CAUTIs. For patients who require an indwelling catheter for operative purposes, the catheter is typically removed within 24 hours or less. Some agencies have a protocol for the removal of indwelling catheters, whereas others require a prescription from a provider. For additional instructions about how to remove an indwelling catheter, see the “ Checklist for Foley Removal .”
When removing an indwelling urinary catheter, it is considered a standard of practice to document the time and track the time of the first void. This information is also communicated during handoff reports. If the patient is unable to void within 4-6 hours and/or complains of bladder fullness, the nurse determines if incomplete bladder emptying is occurring according to agency policy. The ANA has made the following recommendations to assess for incomplete bladder emptying:
- The patient should be prompted to urinate.
- If urination volume is less than 180 mL, the nurse should perform a bladder scan to determine the post-void residual. A bladder scan is a bedside test performed by nurses that uses ultrasonic waves to determine the amount of fluid in the bladder.
- If a bladder scanner is not available, a straight urinary catheterization is performed. [2]
When a urinary catheter is removed, instruct the patient on the following guidelines:
- Increase or maintain fluid intake (unless contraindicated).
- Void when able with the goal to urinate within six hours after removal of the catheter. Inform the nurse of the void so that the amount can be measured and documented.
- Be aware that there may be a mild burning sensation during the first void.
- Report any burning, discomfort, frequency, or small amounts of urine when voiding.
- Report an inability to void, bladder tenderness, or distension.
- American Nurses Association. (n.d.). Streamlined evidence-based RN tool: Catheter associated urinary tract infection (CAUTI) prevention. https://www.nursingworld.org/~4aede8/globalassets/practiceandpolicy/innovation--evidence/clinical-practice-material/cauti-prevention-tool/anacautipreventiontool-final-19dec2014.pdf ↵
- American Nurses Association. (n.d.). Streamlined evidence-based RN tool: Catheter associated urinary tract infection (CAUTI) prevention . https://www.nursingworld.org/~4aede8/globalassets/practiceandpolicy/innovation--evidence/clinical-practice-material/cauti-prevention-tool/anacautipreventiontool-final-19dec2014.pdf ↵


9.2: Static Electricity and Charge- Conservation of Charge
Learning Objectives
- Define electric charge, and describe how the two types of charge interact.
- Describe three common situations that generate static electricity.
- State the law of conservation of charge.
What makes plastic wrap cling? Static electricity. Not only are applications of static electricity common these days, its existence has been known since ancient times. The first record of its effects dates to ancient Greeks who noted more than 500 years B.C. that polishing amber temporarily enabled it to attract bits of straw (see Figure \(\PageIndex{1}\)). The very word electric derives from the Greek word for amber ( electron ).
Many of the characteristics of static electricity can be explored by rubbing things together. Rubbing creates the spark you get from walking across a wool carpet, for example. Static cling generated in a clothes dryer and the attraction of straw to recently polished amber also result from rubbing. Similarly, lightning results from air movements under certain weather conditions. You can also rub a balloon on your hair, and the static electricity created can then make the balloon cling to a wall. We also have to be cautious of static electricity, especially in dry climates. When we pump gasoline, we are warned to discharge ourselves (after sliding across the seat) on a metal surface before grabbing the gas nozzle. Attendants in hospital operating rooms must wear booties with aluminum foil on the bottoms to avoid creating sparks which may ignite the oxygen being used.
Some of the most basic characteristics of static electricity include:
- The effects of static electricity are explained by a physical quantity not previously introduced, called electric charge.
- There are only two types of charge, one called positive and the other called negative.
- Like charges repel, whereas unlike charges attract.
- The force between charges decreases with distance.
How do we know there are two types of electric charge ? When various materials are rubbed together in controlled ways, certain combinations of materials always produce one type of charge on one material and the opposite type on the other. By convention, we call one type of charge “positive”, and the other type “negative.” For example, when glass is rubbed with silk, the glass becomes positively charged and the silk negatively charged. Since the glass and silk have opposite charges, they attract one another like clothes that have rubbed together in a dryer. Two glass rods rubbed with silk in this manner will repel one another, since each rod has positive charge on it. Similarly, two silk cloths so rubbed will repel, since both cloths have negative charge. Figure \(\PageIndex{2}\) shows how these simple materials can be used to explore the nature of the force between charges.
More sophisticated questions arise. Where do these charges come from? Can you create or destroy charge? Is there a smallest unit of charge? Exactly how does the force depend on the amount of charge and the distance between charges? Such questions obviously occurred to Benjamin Franklin and other early researchers, and they interest us even today.
Charge Carried by Electrons and Protons
Franklin wrote in his letters and books that he could see the effects of electric charge but did not understand what caused the phenomenon. Today we have the advantage of knowing that normal matter is made of atoms, and that atoms contain positive and negative charges, usually in equal amounts.
Figure \(\PageIndex{3}\) shows a simple model of an atom with negative electrons orbiting its positive nucleus. The nucleus is positive due to the presence of positively charged protons . Nearly all charge in nature is due to electrons and protons, which are two of the three building blocks of most matter. (The third is the neutron, which is neutral, carrying no charge.) Other charge-carrying particles are observed in cosmic rays and nuclear decay, and are created in particle accelerators. All but the electron and proton survive only a short time and are quite rare by comparison.
The charges of electrons and protons are identical in magnitude but opposite in sign. Furthermore, all charged objects in nature are integral multiples of this basic quantity of charge, meaning that all charges are made of combinations of a basic unit of charge. Usually, charges are formed by combinations of electrons and protons. The magnitude of this basic charge is
\[\left|q_{e}\right|=1.60 \times 10^{-19} \mathrm{C}. \nonumber \]
The symbol \(q\) is commonly used for charge and the subscript \(e\) indicates the charge of a single electron (or proton).
The SI unit of charge is the coulomb (C). The number of protons needed to make a charge of 1.00 C is
\[1.00 \mathrm{C} \times \frac{1 \text { proton }}{1.60 \times 10^{-19} \mathrm{C}}=6.25 \times 10^{18} \text { protons. } \nonumber \]
Similarly, 6.25×10 18 electrons have a combined charge of −1.00 coulomb. Just as there is a smallest bit of an element (an atom), there is a smallest bit of charge. There is no directly observed charge smaller than \(\left|q_{e}\right|\), and all observed charges are integral multiples of \(\left|q_{e}\right|\).
THINGS GREAT AND SMALL: THE SUBMICROSCOPIC ORIGIN OF CHARGE
With the exception of exotic, short-lived particles, all charge in nature is carried by electrons and protons. Electrons carry the charge we have named negative. Protons carry an equal-magnitude charge that we call positive. (See Figure \(\PageIndex{4}\).) Electron and proton charges are considered fundamental building blocks, since all other charges are integral multiples of those carried by electrons and protons. Electrons and protons are also two of the three fundamental building blocks of ordinary matter. The neutron is the third and has zero total charge.
Figure \(\PageIndex{4}\) shows a person touching a Van de Graaff generator and receiving excess positive charge. The expanded view of a hair shows the existence of both types of charges but an excess of positive. The repulsion of these positive like charges causes the strands of hair to repel other strands of hair and to stand up. The further blowup shows an artist’s conception of an electron and a proton perhaps found in an atom in a strand of hair.
The electron seems to have no substructure; in contrast, when the substructure of protons is explored by scattering extremely energetic electrons from them, it appears that there are point-like particles inside the proton. These sub-particles, named quarks, have never been directly observed, but they are believed to carry fractional charges as seen in Figure \(\PageIndex{5}\). Charges on electrons and protons and all other directly observable particles are unitary, but these quark substructures carry charges of either \(-\frac{1}{3}\) or \(+\frac{2}{3}\). There are continuing attempts to observe fractional charge directly and to learn of the properties of quarks, which are perhaps the ultimate substructure of matter.
Separation of Charge in Atoms
Charges in atoms and molecules can be separated—for example, by rubbing materials together. Some atoms and molecules have a greater affinity for electrons than others and will become negatively charged by close contact in rubbing, leaving the other material positively charged. (See Figure \(\PageIndex{6}\).) Positive charge can similarly be induced by rubbing. Methods other than rubbing can also separate charges. Batteries, for example, use combinations of substances that interact in such a way as to separate charges. Chemical interactions may transfer negative charge from one substance to the other, making one battery terminal negative and leaving the first one positive.
No charge is actually created or destroyed when charges are separated as we have been discussing. Rather, existing charges are moved about. In fact, in all situations the total amount of charge is always constant. This universally obeyed law of nature is called the law of conservation of charge .
LAW OF CONSERVATION OF CHARGE
Total charge is constant in any process.
In more exotic situations, such as in particle accelerators, mass, \(\Delta m\), can be created from energy in the amount \(\Delta m=\frac{E}{c^{2}}\). Sometimes, the created mass is charged, such as when an electron is created. Whenever a charged particle is created, another having an opposite charge is always created along with it, so that the total charge created is zero. Usually, the two particles are “matter-antimatter” counterparts. For example, an antielectron would usually be created at the same time as an electron. The antielectron has a positive charge (it is called a positron), and so the total charge created is zero. (See Figure \(\PageIndex{7}\).) All particles have antimatter counterparts with opposite signs. When matter and antimatter counterparts are brought together, they completely annihilate one another. By annihilate, we mean that the mass of the two particles is converted to energy E , again obeying the relationship \(\Delta m=\frac{E}{c^{2}}\). Since the two particles have equal and opposite charge, the total charge is zero before and after the annihilation; thus, total charge is conserved.
MAKING CONNECTIONS: CONSERVATION LAWS
Only a limited number of physical quantities are universally conserved. Charge is one—energy, momentum, and angular momentum are others. Because they are conserved, these physical quantities are used to explain more phenomena and form more connections than other, less basic quantities. We find that conserved quantities give us great insight into the rules followed by nature and hints to the organization of nature. Discoveries of conservation laws have led to further discoveries, such as the weak nuclear force and the quark substructure of protons and other particles.
The law of conservation of charge is absolute—it has never been observed to be violated. Charge, then, is a special physical quantity, joining a very short list of other quantities in nature that are always conserved. Other conserved quantities include energy, momentum, and angular momentum.
Section Summary
- There are only two types of charge, which we call positive and negative.
- Like charges repel, unlike charges attract, and the force between charges decreases with the square of the distance.
- The vast majority of positive charge in nature is carried by protons, while the vast majority of negative charge is carried by electrons.
- The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton.
- An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons.
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The SI unit for charge is the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge \(\left|q_{e}\right|\) is
\[\left|q_{e}\right|=1.60 \times 10^{-19} \mathrm{C}. \nonumber\]
- Whenever charge is created or destroyed, equal amounts of positive and negative are involved.
- Most often, existing charges are separated from neutral objects to obtain some net charge.
- Both positive and negative charges exist in neutral objects and can be separated by rubbing one object with another. For macroscopic objects, negatively charged means an excess of electrons and positively charged means a depletion of electrons.
- The law of conservation of charge ensures that whenever a charge is created, an equal charge of the opposite sign is created at the same time.
Glossary
- electric charge
- a physical property of an object that causes it to be attracted toward or repelled from another charged object; each charged object generates and is influenced by a force called an electromagnetic force
- law of conservation of charge
- states that whenever a charge is created, an equal amount of charge with the opposite sign is created simultaneously
- electron
- a particle orbiting the nucleus of an atom and carrying the smallest unit of negative charge
- proton
- a particle in the nucleus of an atom and carrying a positive charge equal in magnitude and opposite in sign to the amount of negative charge carried by an electron


2.9: Reviewing
- Describe strategies for effective review
Reviewing is the final stage in the academic reading process. All the other steps you’ve taken while reading—previewing, active reading, and summarizing (which we’ll discuss in detail later)—put the content into your head. Reviewing helps seal it in place and makes sure it stays accessible when you need the information later.
For example, when you’re ready to study for an exam, you should:
- Review your notes
- If provided, review the chapter objectives and outline
- Review important information, such as theories, facts, names, dates, and terms
- Review any vocabulary flashcards you created
- Review any study questions you created
- Review your answers to study questions and activities
You can use a variety of strategies to review:
- Quiz yourself using your questions
- Review a chapter map you made while previewing or actively reading
- Expand upon a concept map
- Create vocabulary cards
- Recall the information in writing or out loud
As you review, monitor your learning.
- What do you know well?
- What still needs reinforcement?
The following section shows what it looks like to review a text using the summary notes this reader took in previous reading steps.
In the days after I finish reading the chapter, I need to actively review the information and start to learn it well. Since I used the Cornell two-column note-taking method while I was reading, I decide to quiz myself by covering the right side of my note page and asking myself the questions on the left. If possible, I recite my response aloud or write the answer on a scrap of paper. Then I check my answer against my notes. If I recall the answer correctly, I give myself a checkmark ( ✓ ); if incorrect, I give myself an X ( ✘ ).
| What is a Mistake in contract law? |
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I work through the remainder of my notes in the same way. I repeat this process over several study sessions since I know I won’t have mastered the material after looking at it only once or twice! After a number of review periods, I am able to clearly see which areas I know and where I still need work.
| What is a Mistake in contract law? |
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For variety in my study periods, I might also use my chapter map to test my recall of ideas. I might focus on one major topic and try to recall the sub-points and details related to that topic. Alternatively, I might put a section of the map, such as “Misrepresentation,” onto another page and expand the details there. I might also create vocabulary cards for specific terminology that I need to know. I can easily carry a bundle of cards with me and review when I have a few spare minutes.
Sample vocab card:
Front of card
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MISTAKE (in contract law) |
Back of card
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Definition: a circumstance where parties to a contract have entered an agreement that doesn’t reflect the parties’ actual intentions.
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These different review methods will help me to thoroughly understand and learn my course material. Regular review will also help me monitor my learning, helping me identify what I know well and what still needs work.
Contributors and Attributions
- Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
- PQRST Script. Provided by : Lethbridge College. Located at : www.lethbridgecollege.net/elearningcafe/index.php/pqrst-script. Project : eLearning Cafe. License : CC BY: Attribution
- Annotating a Textbook. Provided by : Excelsior Online Reading Lab. Located at : https://owl.excelsior.edu/orc/what-to-do-while-reading/annotating/annotating-a-textbook/ . License : CC BY: Attribution
- Image of student studying. Authored by : vidhyarthidarpan. Located at : pixabay.com/photos/education-learning-engineering-4796952/. License : Other . License Terms : pixabay.com/service/terms/#license


3.2: Defining the Term "Middle East"
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Culturally-speaking, it is difficult to limit the Middle East to a geographic area with hard borders. Civilizations outside of what is commonly referred to as the “Middle East” made intellectual, cultural and biological imprints in today’s Middle East that are indelible, especially in regard to the waves of migration from Central Asia. Further, North Africa has profound cultural connections through language, religious practices and philosophical discourses. There have been contiguous flows of thought and ideas, whether through the spiritual content of Sufism and Muslim folk practices, or through practices and technologies of law, medicine, education, and food production.
With the exception of Israel, the countries in our definition span from North Africa to Central Asia, and are Muslim-majority countries with large populations speaking one or more of the major Middle Eastern languages (Chapter One). Historically, there have been many definitions, however, which do not correspond to our definition closely, if at all (Center, F. G. E.a). Currently, West Asia, from about the Amu Darya (Oxus) River westward, North Africa, and often Turkey, are usually considered a part of the region. Our definition is one of the more inclusive ones because of the shared languages and may shared religious and cultural practices within the countries listed in the introduction.
In 1902 the term “Middle East” was coined in order to designate the area residing between Egypt and Singapore, comprising major access points to Asia, such as the Suez Canal, the Red Sea, the Persian Gulf, etc. (Center, F.G.E.c). West Asia, where most of the countries of the Middle East reside, used to be called the “Near East”, but the newer term “Middle East” also came into usage in the early part of the 20th century.
The main purpose for covering these definitions in this chapter is to demonstrate that the bases for any of the most commonly used terms, also including “Orient” and simply “the East”, are rooted in European perspectives. These terms center Europe in the geography of the world map. Thus, geographic definitions tended to refer to strategic lands which provided Europeans with access to resources and military advantage, especially India (Center, F.G.E.b).


12.4: Assessing An Articulation Request - Best Practices
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In each discipline the traditions, norms, and body of knowledge of that discipline exercise a broad influence over what is appropriate to cover in introductory, intermediate and advanced levels. Additionally, each institution’s academic governance normally scrutinizes and approves every new course and program, and assesses its suitability for inclusion in the calendar. At the same time, the norms of academic autonomy include the right and responsibility of faculty members to design and teach a course according to their own professional judgment, faculty teaching the same course in the same institution may choose different texts, readings, assignments, exercises, topics and evaluation methods. In the same way, a post-secondary course with the same name or title will not be identical from one institution to another, and the degree of similarity may vary according to the discipline.
Assessing Equivalence
There are several approaches to assessing equivalence.
- Content: There is no universal rule regarding the percentage of match since it is recognized that an appropriate match can vary from discipline to discipline. In some disciplines, where mastery of key concepts is prerequisite to success in subsequent courses, it may be vital to have a substantial match of content in courses. Some institutions or disciplines have developed a rule of thumb for the percentage of match while others make case-by-case judgments. Best practice, however, is to avoid inflexible rules about percentage of match, and to focus on discipline and context-appropriate content.
- Outcomes: Courses can have similar goals, objectives, aims, and outcomes, even if the content varies. For example, two writing courses may use different texts, assignments, instructional styles, methods of delivery, and evaluation and grading practices, and yet have the same goal of teaching students to write at a postsecondary level.
- Level: A course which has no equivalent in the calendar of an institution may still be suitable to satisfy some of the elective requirements of a credential. For example, some institutions may not offer linguistics, criminology, religious studies, archaeology, languages, or courses in applied and professional studies. However, if a course is taught at the appropriate level and the standard expected of students is equivalent to that of the credential to which the credit can be applied, it can be deemed equivalent for the purposes of awarding unassigned or elective transfer credit.
Assessing An Online Course
Evaluating a course for transfer credit involves assessing its equivalence to a specific course at the receiving institution. Evaluators must take a fair and balanced approach to the assessment of all courses, and this should be no different for online courses. The assessment must be based on the variables of equivalence, as outlined above, and delivery mode should only be taken into account if it appears likely that it unduly impacts on the equivalence of the course to possible matching courses at the evaluating institution.
If a realistic assessment is not possible, because of the paucity of information provided by the sending institution or the student, reasonable efforts should be made to request a satisfactory course outline, upon which a sound decision can be based. While the onus for procuring this has often been placed on the student, electronic communication methods have made this easier.
However, the reality is that an evaluator only has so much time for the assessment task, and cannot be expected to hunt down information. Given this, it is fair to reject a request for transfer credit if the evidence presented does not allow for an adequate assessment of equivalence, or raises unanswered questions about the integrity of exams, the hours of learning expected, or any other variable deemed as a sine qua non in a reasonable assessment process.
Awarding Credit
For a student, the best type of transfer credit is assigned credit. Transfer credit is assigned when a course is assessed as being equivalent to a specific course at a receiving institution. For example, College X MATH 111 = University Y MATH 100.
Most credentials require that students complete certain courses at each level. Awarding assigned credit allows students to demonstrate that they have fulfilled requirements. Therefore, it is sound practice to award assigned credit wherever possible.
If the course is appropriate for credit in the discipline, but no close match can be established with a department’s courses, then “unassigned” discipline-specific transfer credit can be awarded. This type of credit verifies that the course is taught at the expected level and standard, that it conforms to the norms of the discipline, and that it is suitable as an elective credit within a degree program. Students can usually use unassigned credit to fulfill general program requirements. More general designations, such as “Arts (3)” or “Humanities (3)” can be used where the receiving institution does not have a corresponding discipline, but the course is identifiable as appropriate for elective credit within a faculty or program. If the course has no corresponding discipline, program, or faculty, but is obviously at the appropriate academic level, the receiving institution can use a designation such as "general elective.” In rare cases, an institution may use this more general designation for a course for which they have a corresponding discipline, but which appears to fall outside the norm for how similar courses are delivered or organized at the institution.
“No credit” is an articulation, and will appear in the institutional or provincial/state transfer guide. Awarding “no credit” means that a student is denied credit for learning achieved, and must replace that credit with additional coursework. This is expensive for the student, the institution, and the system. Where an institution does not offer a similar course or program, every effort should be made to award a minimum of elective credit.
There are two situations in which it is acceptable to award “no credit”.
- The course is not taught at the post-secondary level. A course which appears to be English composition, but which is really English as a Second Language, will be evaluated as being preparatory. Many courses are not designed for transfer (e.g., purely vocational courses such as welding, or preparatory courses such as high school algebra) except to similar programs at other institutions. Occasionally such courses are submitted for articulation in error.
- A "no credit" is appropriate when it is clear that there is no possibility of the student applying credit for the course towards any program at that institution. For example, a specialized course in a technology, a practicum course for a professional program, or a studio or field course in a subject not congruent with the programs at the receiving institution may not be applicable to any credential.
A word about pedagogy: normally, how a course is taught is assumed to be immaterial to the assessment of equivalence, but there are some cases where the manner in which a course is structured and taught is integral to content mastery. For example, at one university, in order to assign a W (“writing intensive”) designation to a course, a committee assesses the nature and number of opportunities for students to write and revise. In some First Nations courses culturally sensitive pedagogy may be inextricably linked to course content. In such cases, best practice requires the receiving institution to communicate its expectations clearly.


14.5: Nuclear Decay and Conservation Laws
Learning Objectives
- Define and discuss nuclear decay.
- State the conservation laws.
- Explain parent and daughter nucleus.
- Calculate the energy emitted during nuclear decay.
Nuclear decay has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.
Some nuclides are stable, apparently living forever. Unstable nuclides decay (that is, they are radioactive), eventually producing a stable nuclide after many decays. We call the original nuclide the parent and its decay products the daughters . Some radioactive nuclides decay in a single step to a stable nucleus. For example, \({ }^{60} \mathrm{Co}\) is unstable and decays directly to \({ }^{60} \mathrm{Ni}\), which is stable. Others, such as \({ }^{238} \mathrm{~u}\), decay to another unstable nuclide, resulting in a decay series in which each subsequent nuclide decays until a stable nuclide is finally produced. The decay series that starts from \({ }^{238} \mathrm{~u}\) is of particular interest, since it produces the radioactive isotopes \({ }^{226} \mathrm{Ra}\) and \({ }^{210} \mathrm{Po}\), which the Curies first discovered (see Figure \(\PageIndex{1}\)). Radon gas is also produced (\({ }^{222} \mathrm{Rn}\) in the series), an increasingly recognized naturally occurring hazard. Since radon is a noble gas, it emanates from materials, such as soil, containing even trace amounts of \({ }^{238} \mathrm{~u}\) and can be inhaled. The decay of radon and its daughters produces internal damage. The \({ }^{238} \mathrm{~u}\) decay series ends with \({ }^{206} \mathrm{~Pb}\), a stable isotope of lead.
Note that the daughters of \(\alpha\) decay shown in Figure \(\PageIndex{1}\) always have two fewer protons and two fewer neutrons than the parent. This seems reasonable, since we know that \(\alpha\) decay is the emission of a \({ }^{4} \mathrm{He}\) nucleus, which has two protons and two neutrons. The daughters of \(\beta\) decay have one less neutron and one more proton than their parent. Beta decay is a little more subtle, as we shall see. No \(\gamma\) decays are shown in the figure, because they do not produce a daughter that differs from the parent.
Alpha Decay
In alpha decay , a \({ }^{4} \mathrm{He}\) nucleus simply breaks away from the parent nucleus, leaving a daughter with two fewer protons and two fewer neutrons than the parent (see Figure \(\PageIndex{2}\)). One example of \(\alpha\) decay is shown in Figure \(\PageIndex{1}\) for \({ }^{238} \mathrm{~u}\). Another nuclide that undergoes \(\alpha\) decay is \({ }^{239} \mathrm{Pu}\). The decay equations for these two nuclides are
\[{ }^{238} \mathrm{~u} \rightarrow{ }^{234} \mathrm{Th}_{92}^{234}+{ }^{4} \mathrm{He} \nonumber \]
and
\[{ }^{239} \mathrm{Pu} \rightarrow{ }^{235} \mathrm{~u}+{ }^{4} \mathrm{He}. \nonumber \]
If you examine the periodic table of the elements, you will find that Th has \(Z=90\), two fewer than U, which has \(Z=92\). Similarly, in the second decay equation , we see that U has two fewer protons than Pu, which has \(Z=94\). The general rule for \(\alpha\) decay is best written in the format \({ }_{Z}^{A} \mathrm{X}_{N}\). If a certain nuclide is known to \(\alpha\) decay (generally this information must be looked up in a table of isotopes, such as in Appendix B), its \(\alpha\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z-2}^{A-4} \mathrm{Y}_{N-2}+{ }_{2}^{4} \mathrm{He}_{2} \quad(\alpha \text { decay }) \nonumber \]
where Y is the nuclide that has two fewer protons than X, such as Th having two fewer than U. So if you were told that \({ }^{239} \mathrm{Pu}\) \(\alpha\) decays and were asked to write the complete decay equation, you would first look up which element has two fewer protons (an atomic number two lower) and find that this is uranium. Then since four nucleons have broken away from the original 239, its atomic mass would be 235.
It is instructive to examine conservation laws related to \(\alpha\) decay. You can see from the equation \({ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z-2}^{A-4} \mathrm{Y}_{N-2}+{ }_{2}^{4} \mathrm{He}_{2}\) that total charge is conserved. Linear and angular momentum are conserved, too. Although conserved angular momentum is not of great consequence in this type of decay, conservation of linear momentum has interesting consequences. If the nucleus is at rest when it decays, its momentum is zero. In that case, the fragments must fly in opposite directions with equal-magnitude momenta so that total momentum remains zero. This results in the \(\alpha\) particle carrying away most of the energy, as a bullet from a heavy rifle carries away most of the energy of the powder burned to shoot it. Total mass–energy is also conserved: the energy produced in the decay comes from conversion of a fraction of the original mass. The general relationship is
\[E=(\Delta m) c^{2}. \nonumber \]
Here, \(E\) is the nuclear reaction energy (the reaction can be nuclear decay or any other reaction), and \(\Delta m\) is the difference in mass between initial and final products. When the final products have less total mass, \(\Delta m\) is positive, and the reaction releases energy (is exothermic). When the products have greater total mass, the reaction is endothermic (\(\Delta m\) is negative) and must be induced with an energy input. For \(\alpha\) decay to be spontaneous, the decay products must have smaller mass than the parent.
Example \(\PageIndex{1}\): Alpha Decay Energy Found from Nuclear Masses
Find the energy emitted in the \(\alpha\) decay of \({ }^{239} \mathrm{Pu}\).
Strategy
Nuclear reaction energy, such as released in \(\alpha\) decay, can be found using the equation \(E=(\Delta m) c^{2}\). We must first find \(\Delta m\), the difference in mass between the parent nucleus and the products of the decay. This is easily done using masses given in Appendix A.
Solution
The decay equation was given earlier for \({ }^{239} \mathrm{Pu}\) ; it is
\[{ }^{239} \mathrm{Pu} \rightarrow{ }^{235} \mathrm{~u}+{ }^{4} \mathrm{He}. \nonumber\]
Thus the pertinent masses are those of \({ }^{239} \mathrm{Pu}\), \({ }^{235} \mathrm{~u}\), and the \(\alpha\) particle or \({ }^{4} \mathrm{He}\), all of which are listed in Appendix A. The initial mass was \(m\left({ }^{239} \mathrm{Pu}\right)=239.052157 \mathrm{~u}\). The final mass is the sum \(m\left({ }^{235} \mathrm{~u}\right)+m\left({ }^{4} \mathrm{He}\right)=235.043924 \mathrm{~u}+4.002602 \mathrm{~u}=239.046526 \mathrm{~u} \). Thus,
\[\begin{aligned}
\Delta m &=m\left({ }^{239} \mathrm{Pu}\right)-\left[m\left({ }^{235} \mathrm{~u}\right)+m\left({ }^{4} \mathrm{He}\right)\right] \\
&=239.052157 \mathrm{~u}-239.046526 \mathrm{~u} \\
&=0.005631 \mathrm{~u} .
\end{aligned} \nonumber\]
Now we can find \(E\) by entering \(\Delta m\) into the equation:
\[E=(\Delta m) c^{2}=(0.005631 \mathrm{~u}) c^{2}. \nonumber \]
We know \(1 \mathrm{~u}=931.5 \mathrm{~MeV} / c^{2}\), and so
\[E=(0.005631)\left(931.5 \mathrm{~MeV} / c^{2}\right)\left(c^{2}\right)=5.25 \mathrm{~MeV}. \nonumber\]
Discussion
The energy released in this \(\alpha\) decay is in the \(\mathrm{~MeV}\) range, about \(10^{6}\) times as great as typical chemical reaction energies, consistent with many previous discussions. Most of this energy becomes kinetic energy of the \(\alpha\) particle (or \({ }^{4} \mathrm{He}\) nucleus), which moves away at high speed. The energy carried away by the recoil of the \({ }^{235} \mathrm{~u}\) nucleus is much smaller in order to conserve momentum. The \({ }^{235} \mathrm{~u}\) nucleus can be left in an excited state to later emit photons (\(\gamma\) rays). This decay is spontaneous and releases energy, because the products have less mass than the parent nucleus. The question of why the products have less mass will be discussed in "Binding Energy." Note that the masses given in Appendix A are atomic masses of neutral atoms, including their electrons. The mass of the electrons is the same before and after \(\alpha\) decay, and so their masses subtract out when finding \(\Delta m\). In this case, there are 94 electrons before and after the decay.
Beta Decay
There are actually three types of beta decay . The first discovered was “ordinary” beta decay and is called \(\beta^{-}\) decay or electron emission. The symbol \(\beta^{-}\) represents an electron emitted in nuclear beta decay . Cobalt-60 is a nuclide that \(\beta^{-}\) decays in the following manner:
\[{ }^{60} \mathrm{Co} \rightarrow{ }^{60} \mathrm{Ni}+\beta^{-}+\text {neutrino. } \nonumber \]
The neutrino is a particle emitted in beta decay that was unanticipated and is of fundamental importance. The neutrino was not even proposed in theory until more than 20 years after beta decay was known to involve electron emissions. Neutrinos are so difficult to detect that the first direct evidence of them was not obtained until 1953. Neutrinos are nearly massless, have no charge, and do not interact with nucleons via the strong nuclear force. Traveling approximately at the speed of light, they have little time to affect any nucleus they encounter. This is, owing to the fact that they have no charge (and they are not EM waves), they do not interact through the EM force. They do interact via the relatively weak and very short range weak nuclear force. Consequently, neutrinos escape almost any detector and penetrate almost any shielding. However, neutrinos do carry energy, angular momentum (they are fermions with half-integral spin), and linear momentum away from a beta decay. When accurate measurements of beta decay were made, it became apparent that energy, angular momentum, and linear momentum were not accounted for by the daughter nucleus and electron alone. Either a previously unsuspected particle was carrying them away, or three conservation laws were being violated. Wolfgang Pauli made a formal proposal for the existence of neutrinos in 1930. The Italian-born American physicist Enrico Fermi (1901–1954) gave neutrinos their name, meaning little neutral ones, when he developed a sophisticated theory of beta decay (see Figure \(\PageIndex{3}\)). Part of Fermi’s theory was the identification of the weak nuclear force as being distinct from the strong nuclear force and in fact responsible for beta decay.
The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. So electrons are given an electron family number of \(+1\). The neutrino in \(\beta^{-}\) decay is an electron’s antineutrino , given the symbol \(\bar{\nu}_{e}\), where \(\nu\) is the Greek letter nu, and the subscript \(e\) means this neutrino is related to the electron. The bar indicates this is a particle of antimatter . (All particles have antimatter counterparts that are nearly identical except that they have the opposite charge. Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space.) The electron’s antineutrino \(\bar{\nu}_{e}\), being antimatter, has an electron family number of \(–1\). The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the total electron family number is constant . An electron cannot be created without also creating an antimatter family member. This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.
If a nuclide \({ }_{Z}^{A} \mathrm{X}_{N}\) is known to \(\beta^{-}\) decay, then its \(\beta^{-}\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z+1}^{A} \mathrm{Y}_{N-1}+\beta^{-}+\bar{\nu}_{e}\left(\beta^{-} \text {decay }\right), \nonumber \]
where \(Y\) is the nuclide having one more proton than X (see Figure \(\PageIndex{4}\)). So if you know that a certain nuclide \(\beta^{-}\) decays, you can find the daughter nucleus by first looking up \(Z\) for the parent and then determining which element has atomic number \(Z+1\). In the example of the \(\beta^{-}\) decay of \({ }^{60} \mathrm{Co}\) given earlier, we see that \(Z=27\) for Co and \(Z=28\) is Ni. It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. In fact, neutrons outside of nuclei do just that—they live only an average of a few minutes and \(\beta^{-}\) decay in the following manner:
\[\mathrm{n} \rightarrow \mathrm{p}+\beta^{-}+\bar{\nu}_{e}. \nonumber \]
We see that charge is conserved in \(\beta^{-}\) decay, since the total charge is \(Z\) before and after the decay. For example, in \({ }^{60} \mathrm{Co}\) decay, total charge is 27 before decay, since cobalt has \(Z=27\). After decay, the daughter nucleus is Ni, which has \(Z=28\), and there is an electron, so that the total charge is also \(28+(-1)\) or \(27\). Angular momentum is conserved, but not obviously (you have to examine the spins and angular momenta of the final products in detail to verify this). Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. The total number of nucleons A is conserved . In \({ }^{60} \mathrm{Co}\) decay, for example, there are 60 nucleons before and after the decay. Note that total A is also conserved in \(\alpha\) decay. Also note that the total number of protons changes, as does the total number of neutrons, so that total \(Z\) and total \(N\) are not conserved in \(\beta^{-}\) decay, as they are in \(\alpha\) decay. Energy released in \(\beta^{-}\) decay can be calculated given the masses of the parent and products.
Example \(\PageIndex{2}\): \(\beta\)− Decay Energy from Masses
Find the energy emitted in the \(\beta^{-}\) decay of \({ }^{60} \mathrm{Co}\).
Strategy and Concept
As in the preceding example, we must first find \(\Delta m\), the difference in mass between the parent nucleus and the products of the decay, using masses given in Appendix A. Then the emitted energy is calculated as before, using \(E=(\Delta m) c^{2}\). The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. However, since the masses given in Appendix A are for neutral atoms, the daughter nucleus has one more electron than the parent, and so the extra electron mass that corresponds to the \(\beta^{-}\) is included in the atomic mass of Ni. Thus,
\[\Delta m=m\left({ }^{60} \mathrm{Co}\right)-m\left({ }^{60} \mathrm{Ni}\right). \nonumber \]
Solution
The \(\beta^{-}\) decay equation for \({ }^{60} \mathrm{Co}\) is
\[{ }_{27}^{60} \mathrm{Co}_{33} \rightarrow{ }_{28}^{60} \mathrm{Ni}_{32}+\beta^{-}+\bar{\nu}_{e}. \nonumber \]
As noticed,
\[\Delta m=m\left({ }^{60} \mathrm{Co}\right)-m\left({ }^{60} \mathrm{Ni}\right) \text {. } \nonumber\]
Entering the masses found in Appendix A gives
\[\Delta m=59.933820 \mathrm{~u}-59.930789 \mathrm{~u}=0.003031 \mathrm{~u} . \nonumber\]
Thus,
\[E=(\Delta m) c^{2}=(0.003031 \mathrm{~u}) c^{2}. \nonumber\]
Using \(1 \mathrm{~u}=931.5 \mathrm{~MeV} / c^{2}\), we obtain
\[E=(0.003031)\left(931.5 \mathrm{~MeV} / c^{2}\right)\left(c^{2}\right)=2.82 \mathrm{~MeV} . \nonumber\]
Discussion and Implications
Perhaps the most difficult thing about this example is convincing yourself that the \(\beta^{-}\) mass is included in the atomic mass of \({ }^{60} \mathrm{Ni}\). Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay. In many \({ }^{60} \mathrm{Co}\) decays, the daughter nucleus \({ }^{60} \mathrm{Ni}\) is left in an excited state and emits photons ( \(\gamma\) rays). Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. One final note: the electron emitted in \(\beta^{-}\) decay is created in the nucleus at the time of decay.
The second type of beta decay is less common than the first. It is \(\beta^{+}\) decay. Certain nuclides decay by the emission of a positive electron. This is antielectron or positron decay (see Figure \(\PageIndex{5}\)).
The antielectron is often represented by the symbol \(e^{+}\), but in beta decay it is written as \(\beta^{+}\) to indicate the antielectron was emitted in a nuclear decay. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of –1. When a positron encounters an electron, there is a mutual annihilation in which all the mass of the antielectron-electron pair is converted into pure photon energy. (The reaction, \(e^{+}+e^{-} \rightarrow \gamma+\gamma\), conserves electron family number as well as all other conserved quantities.) If a nuclide \({ }_{Z}^{A} \mathrm{X}_{N}\) is known to \(\beta^{+}\) decay, then its \(\beta^{+}\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z-1}^{A} \mathrm{Y}_{N+1}+\beta^{+}+\nu_{e}\left(\beta^{+} \text {decay }\right), \nonumber \]
where \(Y\) is the nuclide having one less proton than \(X\) (to conserve charge) and \(\nu_{e}\) is the symbol for the electron’s neutrino , which has an electron family number of \(+1\). Since an antimatter member of the electron family (the \(\beta^{+}\)) is created in the decay, a matter member of the family (here the \(\nu_{e}\)) must also be created. Given, for example, that \({ }^{22} \mathrm{Na}\) \(\beta^{+}\) decays, you can write its full decay equation by first finding that \(Z=11\) for \({ }^{22} \mathrm{Na}\), so that the daughter nuclide will have \(Z=10\), the atomic number for neon. Thus the \(\beta^{+}\) decay equation for \({ }^{22} \mathrm{Na}\) is
\[{ }_{11}^{22} \mathrm{Na}_{11} \rightarrow{ }_{10}^{22} \mathrm{Ne}_{12}+\beta^{+}+\nu_{e}. \nonumber \]
In \(\beta^{+}\) decay, it is as if one of the protons in the parent nucleus decays into a neutron, a positron, and a neutrino. Protons do not do this outside of the nucleus, and so the decay is due to the complexities of the nuclear force. Note again that the total number of nucleons is constant in this and any other reaction. To find the energy emitted in \(\beta^{+}\) decay, you must again count the number of electrons in the neutral atoms, since atomic masses are used. The daughter has one less electron than the parent, and one electron mass is created in the decay. Thus, in \(\beta^{+}\) decay,
\[\Delta m=m(\text { parent })-\left[m \text { (daughter) }+2 m_{e}\right], \nonumber \]
since we use the masses of neutral atoms.
Electron capture is the third type of beta decay. Here, a nucleus captures an inner-shell electron and undergoes a nuclear reaction that has the same effect as \(\beta^{+}\) decay. Electron capture is sometimes denoted by the letters EC. We know that electrons cannot reside in the nucleus, but this is a nuclear reaction that consumes the electron and occurs spontaneously only when the products have less mass than the parent plus the electron. If a nuclide \({ }_{Z}^{A} \mathrm{X}_{N}\) is known to undergo electron capture, then its electron capture equation is
\[{ }_{Z}^{A} \mathrm{X}_{N}+e^{-} \rightarrow{ }_{Z-1}^{A} \mathrm{Y}_{N+1}+\nu_{e}(\text { electron capture, or EC }). \nonumber \]
Any nuclide that can \(\beta^{+}\) decay can also undergo electron capture (and often does both). The same conservation laws are obeyed for EC as for \(\beta^{+}\) decay. It is good practice to confirm these for yourself.
All forms of beta decay occur because the parent nuclide is unstable and lies outside the region of stability in the chart of nuclides. Those nuclides that have relatively more neutrons than those in the region of stability will \(\beta^{-}\) decay to produce a daughter with fewer neutrons, producing a daughter nearer the region of stability. Similarly, those nuclides having relatively more protons than those in the region of stability will \(\beta^{-}\) decay or undergo electron capture to produce a daughter with fewer protons, nearer the region of stability.
Gamma Decay
Gamma decay is the simplest form of nuclear decay—it is the emission of energetic photons by nuclei left in an excited state by some earlier process. Protons and neutrons in an excited nucleus are in higher orbitals, and they fall to lower levels by photon emission (analogous to electrons in excited atoms). Nuclear excited states have lifetimes typically of only about \(10^{-14}\) s, an indication of the great strength of the forces pulling the nucleons to lower states. The \(\gamma\) decay equation is simply
\[{ }_{Z}^{A} \mathrm{X}_{N}^{*} \rightarrow{ }_{Z}^{A} \mathrm{X}_{N}+\gamma_{1}+\gamma_{2}+\cdots(\gamma \text { decay }) \nonumber \]
where the asterisk indicates the nucleus is in an excited state. There may be one or more \(\gamma\)s emitted, depending on how the nuclide de-excites. In radioactive decay, \(\gamma\) emission is common and is preceded by \(\gamma\) or \(\beta\) decay. For example, when \({ }^{60} \mathrm{Co}\) \(\beta^{-}\) decays, it most often leaves the daughter nucleus in an excited state, written \({ }^{60} \mathrm{Ni}^{*}\). Then the nickel nucleus quickly \(\gamma\) decays by the emission of two penetrating \(\gamma\)s:
\[{ }^{60} \mathrm{Ni}^{*} \rightarrow{ }^{60} \mathrm{Ni}+\gamma_{1}+\gamma_{2}. \nonumber \]
These are called cobalt \(\gamma\) rays, although they come from nickel—they are used for cancer therapy, for example. It is again constructive to verify the conservation laws for gamma decay. Finally, since \(\gamma\) decay does not change the nuclide to another species, it is not prominently featured in charts of decay series, such as that in Figure \(\PageIndex{1}\).
There are other types of nuclear decay, but they occur less commonly than \(\alpha\), \(\beta\), and \(\gamma\) decay. Spontaneous fission is the most important of the other forms of nuclear decay because of its applications in nuclear power and weapons. It is covered in the next chapter.
Section Summary
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When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha (\(\alpha\)), beta (\(\beta\)), and gamma (\(\gamma\)). The \(\alpha\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z-2}^{A-4} \mathrm{Y}_{N-2}+{ }_{2}^{4} \mathrm{He}_{2}. \nonumber\]
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Nuclear decay releases an amount of energy \(E\) related to the mass destroyed \(\Delta m\) by
\[E=(\Delta m) c^{2}. \nonumber\]
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There are three forms of beta decay. The \(\beta^{-}\)decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z+1}^{A} \mathrm{Y}_{N-1}+\beta^{-}+\bar{\nu}_{e}. \nonumber\]
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The \(\beta^{+}\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N} \rightarrow{ }_{Z-1}^{A} \mathrm{Y}_{N+1}+\beta^{+}+\nu_{e}. \nonumber\]
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The electron capture equation is
\[{ }_{Z}^{A} \mathrm{X}_{N}+e^{-} \rightarrow{ }_{Z-1}^{A} \mathrm{Y}_{N+1}+\bar{\nu}_{e}. \nonumber\]
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\(\beta^{-}\) is an electron, \(\beta^{+}\) is an antielectron or positron, \(\nu_{e}\) represents an electron’s neutrino, and \(\bar{\nu}_{e}\) is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of nucleons. The \(\gamma\) decay equation is
\[{ }_{Z}^{A} \mathrm{X}_{N}^{*} \rightarrow{ }_{Z}^{A} \mathrm{X}_{N}+\gamma_{1}+\gamma_{2}+\cdots \nonumber\]
\(\gamma\) is a high-energy photon originating in a nucleus.
Glossary
- parent
- the original state of nucleus before decay
- daughter
- the nucleus obtained when parent nucleus decays and produces another nucleus following the rules and the conservation laws
- positron
- the particle that results from positive beta decay; also known as an antielectron
- decay
- the process by which an atomic nucleus of an unstable atom loses mass and energy by emitting ionizing particles
- alpha decay
- type of radioactive decay in which an atomic nucleus emits an alpha particle
- beta decay
- type of radioactive decay in which an atomic nucleus emits a beta particle
- gamma decay
- type of radioactive decay in which an atomic nucleus emits a gamma particle
- decay equation
- the equation to find out how much of a radioactive material is left after a given period of time
- nuclear reaction energy
- the energy created in a nuclear reaction
- neutrino
- an electrically neutral, weakly interacting elementary subatomic particle
- electron’s antineutrino
- antiparticle of electron’s neutrino
- positron decay
- type of beta decay in which a proton is converted to a neutron, releasing a positron and a neutrino
- antielectron
- another term for positron
- decay series
- process whereby subsequent nuclides decay until a stable nuclide is produced
- electron’s neutrino
- a subatomic elementary particle which has no net electric charge
- antimatter
- composed of antiparticles
- electron capture
- the process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino
- electron capture equation
- equation representing the electron capture