   Chapter 31, Problem 29PE

Chapter
Section
Textbook Problem

When an electron and position annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation e + + e − → γ + γ conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each γ ray, assuming the election and positron are initially nearly at rest. (c) Explain why the two γ rays travel in exactly opposite directions if the center at mass of the electron—positron system is initially at rest.

To determine

(a)

To prove:

The e++e-γ+γconserves charges, electron family number and total number of nucleons.

Explanation

Given:

Charge on

e+=+1e-=1

Formula used:

Total Charge = Positive charge + negative charge, Total electron family number = positive family number + negative family numberTotal number of nucleons = positive nucleons + negative nucleons

Calculation:

Substituting the values of charges in the above equation we get:

Total Charge = Positive charge

To determine

(b)

Energy of each gamma ray

To determine

(c)

The reason for two gamma rays that will travel in exactly opposite directions if the center of mass of the electron-positron system in initially at rest.

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