Solving Nuclear Physics Revision Questions: Li and Be

In summary, Peter identified the unstable nucleus as the Be nucleus, and explained how it decays into the Li nucleus. Homework Equations were also provided.
  • #1
peterjaybee
62
0
Hello, I am having issues with some nuclear physics revision questions

Homework Statement



The following atomic masses have been determined (in Atomic mass units, u) (A = atomic mass number, Z = proton number)
Li(A=7,Z=3) - 7.0182 u
Be(A=7,Z=4) - 7.0192 u
Indicate the stable nucleus and determine its mode(s) of decay.


Homework Equations





The Attempt at a Solution



Ok I have approached this knowing the answer, but not understanding it. The Be nucleus is unstable and decays into the Li, most likely by electron capture.

My problem is I do not understant how to identify the unstable nucleus without reading the answer. The only thing I have noticed which may or may not be relevant is that both nuclei have the same mass number, A, making them isobars.

Can someone please explain how to identify the unstable nucleus?

Many thanks,

Peter
 
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  • #2
The only thing I notice is that the beryllium atom has a slightly greater mass (by 0.001 u) than the lithium atom. When particles decay they lose mass, they don't gain it.
 
  • #3
Modern Physics by Tipler/Llewellyn (4th ed.) has a good overview of nuclear physics. On pp. 516-518 they have a good discussion of nuclear stability.

The short of it is this: for light elements (like Li and Be), the most stable ratio of nucleons is roughly 1:1. Both neutrons and protons are fermions, so the exclusion principle makes it very energetically unfavorable to have a nucleus composed of purely protons or purely neutrons, hence the stability when they're about half and half. With heavier elements, Coulombic interactions among the protons becomes very significant, such that the population of neutrons becomes noticeably larger than that of protons. For example, uranium-238 [the most stable isotope of uranium] has 92 protons and 146 neutrons.

So in the case of your problem, we have an odd number of nucleons, so we can pick either 3 neutrons/4 protons (Be) or 4 neutrons/3 protons (Li). To minimize Coulombic repulsion, pick the one with fewer protons as the stable nucleus. As for which reaction it undergoes, there are only four common ones (alpha, beta+, beta-, and electron capture). Pick the one that gives you the correct change in A and Z, and if there is more than one that could do so, use conservation laws to figure out if one is more favorable than the other.
 
  • #4
Thanks to both of you, I shall go in search of that book in the morning.
 

1. How do you solve nuclear physics revision questions for Li and Be?

To solve nuclear physics revision questions for Li and Be, you first need to understand the basic principles of nuclear physics, such as nuclear reactions, decay processes, and binding energy. Then, you can use equations and concepts such as mass-energy equivalence, nuclear forces, and conservation laws to solve specific problems related to Li and Be nuclei.

2. What are the common mistakes to avoid when solving nuclear physics revision questions for Li and Be?

Some common mistakes to avoid when solving nuclear physics revision questions for Li and Be include using incorrect equations, not paying attention to units and conversions, and forgetting to account for all relevant particles in a nuclear reaction. It is also important to carefully read and understand the question before attempting to solve it.

3. How can I improve my understanding of nuclear physics when revising for Li and Be questions?

To improve your understanding of nuclear physics when revising for Li and Be questions, you can practice solving different types of problems and familiarize yourself with common equations and concepts. It can also be helpful to seek guidance from a teacher or tutor and use online resources or textbooks for additional explanations and examples.

4. What are some real-life applications of nuclear physics concepts related to Li and Be?

Nuclear physics concepts related to Li and Be have various real-life applications, such as in nuclear power plants for generating electricity, in medical imaging and treatment techniques, and in research for developing new materials and technologies. Understanding these concepts can also help us better understand the formation and evolution of stars and galaxies.

5. How can I check my answers when solving nuclear physics revision questions for Li and Be?

You can check your answers when solving nuclear physics revision questions for Li and Be by double-checking your calculations and ensuring that your final answer has the correct units. You can also compare your answer to the given solution or ask for feedback from a teacher or tutor. Additionally, practicing with a variety of problems can help you become more confident in your approach and accuracy when solving these types of questions.

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