# Mathematical problem from the course of reactor physics

• phys_g
In summary, the problem is asking for the smallest value of A for which the maximum fractional energy loss can be approximated by 4/A within a 1% error. The relevant equation is given and the process of differentiation and equating the outcome with zero is suggested. However, this may require studying the series convergence and there is confusion on how to approach the problem. An error bound is also mentioned, with the advice to seek help from Dick.
phys_g
Hello everybody,

This problem is from "Elementary Introduction to Nuclear Reactor Physics" by Liverhant,
I will be thankful for any help,because I'm really stuck on it :(
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(6-11)Calculate the smallest value of A for which the maximum fractional energy loss can be approximated by 4/A to within an error of 1%.
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the ans. should be 200.

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the relevant equation is:

$$\ ( \frac{\Delta E }{E0} )max.=\frac{4}{A} -\frac{8}{A^{2}}+\frac{12}{A^{3}}-\frac{16}{A^{4}}+... = (\frac{4}{A})(1-\frac{2}{A}+\frac{3}{A^{2}}-...)$$

it looks easy but I couldn't get the right answer...
I tried to differentiate this eq. then equate the outcome with zero (to get the smallest value of A), but also I might need to study the series convergence (the radius of convergence must take the value of 1% ...right?)..I'm confused and don't know how to start..because non of these ideas got me the right answer.

I'll appreciate it if anyone can help me in solving this problem either analytically or numerically.

Last edited:
The series is alternating in sign and the terms are decreasing in magnitude. An error bound for such alternating series is that if S is the sum of the whole series with terms a_i, and S_k is the sum of the first k terms, then |S-S_k|<=|a_{k+1}|.

Thanks Dick!

## 1. What is reactor physics and why is it important?

Reactor physics is the study of the behavior and characteristics of nuclear reactors. It is important because it helps us understand how reactors work and how to design and operate them safely and efficiently.

## 2. What types of mathematical problems are commonly encountered in reactor physics?

Common mathematical problems in reactor physics include solving differential equations, performing numerical simulations, and analyzing data using statistical methods. These problems are used to model and predict the behavior of reactors and to optimize their performance.

## 3. How does reactor physics use mathematics to solve complex problems?

Reactor physics uses various mathematical tools such as calculus, linear algebra, and probability theory to describe and solve complex problems. These tools help us understand the physical processes happening in reactors and make accurate predictions about their behavior.

## 4. How does reactor physics involve both theoretical and practical aspects?

Reactor physics involves both theoretical and practical aspects. Theoretical aspects involve using mathematical models and equations to describe and predict the behavior of reactors, while practical aspects involve designing and operating reactors based on these theoretical principles.

## 5. What are some real-world applications of reactor physics?

Reactor physics has a wide range of real-world applications, including nuclear power generation, nuclear weapons development, and nuclear medicine. It is also used in research and development of new reactor designs, nuclear waste management, and radiation detection and protection.

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