Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 12

A particular nuclide is found to have lost 3 neutrons and 1 proton after a decay chain. What combination of \(\alpha\) and \(\beta\) decays could account for this result?

Short Answer

Expert verified
Answer: The combination of decays that can result in the loss of 3 neutrons and 1 proton is 1 alpha decay and 1 beta decay.

Step by step solution

01

Determine the decay chain equation

Let the combination of alpha decays be represented by 'a' and the combination of beta decays be represented by 'b'. Since in an alpha decay, a nucleus loses 2 protons and 2 neutrons, the total loss of protons in 'a' alpha decays is 2a. In a beta decay, a neutron turns into a proton, so the total gain of protons in 'b' beta decays is b. For the entire decay chain, the loss of 1 proton can be represented by the following equation: 2a - b = 1 Similarly, for neutrons, the total loss of neutrons in 'a' alpha decays is 2a, and the total loss of neutrons in 'b' beta decays is b. The total loss of 3 neutrons in the entire decay chain is represented by the following equation: 2a + b = 3
02

Solve the system of equations

Now, we have a system of two linear equations with two variables, a and b: 1) 2a - b = 1 2) 2a + b = 3 We can solve these equations using different methods, but let's use the elimination method. Add equation (1) and equation (2) to eliminate the 'b' variable: 2a - b + 2a + b = 1 + 3 4a = 4 Now, let's solve for 'a': a = 4/4 a = 1 To find the value of 'b', substitute the value of 'a' into either equation, such as equation (1): 2(1) - b = 1 2 - b = 1 b = 1
03

Final result

The combination of alpha (a) and beta (b) decays that can account for the loss of 3 neutrons and 1 proton after a decay chain is: a = 1 (one alpha decay) b = 1 (one beta decay)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain in some detail what happens if control rods are too effective at absorbing neutrons so that each fission event produces too few unabsorbed neutrons.

If a nuclear plant is built for \(\$ 10\) billion and operates for 50 years under an operating cost of \(\$ 100\) million per year, what is the cost to produce electricity, in \(\$ / \mathrm{kWh}\) assuming that the plant delivers power at a steady rate of \(1 \mathrm{GW}\) for the whole time?

In close analog to the half-lives of \({ }^{235} \mathrm{U}\) and \({ }^{238} \mathrm{U}\), let's say two 80 elements have half lives of \(4.5\) billion years and 750 million years. If we start out having the same number of each (1:1 ratio), what will the ratio be after \(4.5\) billion years? Express as \(x: 1\), where \(x\) is the larger of the two.

Which of the following is true about the fragments from \(\mathrm{a}^{235} \mathrm{U}\) fission event? a) any number of fragments ( 2 through 235 ) can be produced b) a small number of fragments will emerge ( 2 to 5 ) c) two nearly identical fragments will emerge d) two fragments of distinctly different size will emerge e) the fission is an alpha decay: a small piece having \(A=4\) is emitted

Based on the calculation that 18 TW would require an annual cube of seawater \(300 \mathrm{~m}\) on a side to provide enough deuterium, what is your personal share as one of 8 billion people on earth, in liters? Could you lift this yourself? One cubic meter is \(1,000 \mathrm{~L}\).
See all solutions

Recommended explanations on Environmental Science Textbooks

Physical Environment

Read Explanation

Biological Resources

Read Explanation

Environmental Research

Read Explanation

Energy Resources

Read Explanation

Pollution

Read Explanation

Environmental Policy

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free