/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Beta decay by positron emission ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 38: Problem 4

Beta decay by positron emission is soon followed by a pair of 511 -keV gamma rays. Why?

Short Answer

Expert verified
The emission of a positron during beta decay is soon followed by a pair of 511-keV gamma rays due to the annihilation of the positron with an electron. This annihilation turns the rest mass energy of both particles into energy of motion, resulting in the emission of two equal-energy gamma rays, each of 511 keV.

Step by step solution

01

Nuclear Decay Process

During beta decay by positron emission, a proton inside a nucleus is converted into a neutron, a positron \(e^{+}\), and a neutrino. The positron is emitted from the nucleus.
02

Post-Decay Interaction

The newly emitted positron will travel a short distance, typically within the same material, until it encounters an electron. When the positron meets an electron, they annihilate each other.
03

Conservation of Energy and Momentum

In the annihilation, the complete rest mass energy of both particles is converted into energy of motion, in accordance with Einstein's equation \(E=mc^2\). As electrons and positrons have rest mass energy of 511 keV each, the total energy released in the annihilation is 1022 keV. This energy is carried away by two gamma rays to satisfy both energy and momentum conservation. Each of these gamma rays has an energy of 511 keV, the rest mass energy of an electron or positron.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

Of the neutrons emitted in each fission event in a light-water reactor, an average of 0.6 neutron is absorbed by \(^{238} \mathrm{U}\), leading to the formation of \(^{239} \mathrm{Pu}\). (a) Assuming 200 MeV per fission, how much \(^{239}\) Pu forms each year in a \(30 \%\) -efficient nuclear plant whose electric power output is \(1.0 \mathrm{GW} ?\) (b) With careful design, a fission explosive can be made from \(5 \mathrm{kg}\) of \(^{239} \mathrm{Pu}\). How many potential bombs are produced each year in the power plant of part (a)?

Find the atomic mass of iridium-193, whose binding energy is 7.94 MeV/nucleon.

Why do nuclei contain neutrons?

Write a complete equation for neutron-induced fission of plutonium-239 that yields barium-143, two neutrons, and another nucleus.

You're assessing the safety of an airport bomb-detection system in which neutron activation of the stable nitrogen isotope \(^{15} 7 \mathrm{N}\) turns it into unstable \(^{16}\) ?N. The N-16 decays by beta emission with 7.13-s half-life. How long after activation will the \(\mathbf{N}-16\) activity have dropped by a factor of 1 million?
See all solutions

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Read Explanation

Quantum Physics

Read Explanation

Force

Read Explanation

Famous Physicists

Read Explanation

Fluids

Read Explanation

Classical Mechanics

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.