   Chapter 19, Problem 66AE

Chapter
Section
Textbook Problem

# A positron and an electron can annihilate each other on colliding, producing energy as photons: e − 1 0   +   e + 1 0   →   2   γ 0 0 Assuming that both γ rays have the same energy, calculate the wavelength of the electromagnetic radiation produced.

Interpretation Introduction

Interpretation: Production of energy as photons when a positron and an electron annihilate each other is given. Assuming the both gamma rays have the same energy, the wavelength of the electromagnetic radiation produced is to be calculated.

Concept introduction: Positron is an antiparticle of electron. When they both meet, they annihilate each other by the production of gamma rays. There is conservation of electric charge, linear momentum and total energy during the annihilation process.

To determine: The wavelength of the electromagnetic radiation produced.

Explanation

Explanation

The mass of electron =9.1×1031kg

Since reactants involve a positron and an electron.

Therefore the change in mass, Δm is

Δm=2×9.1×1031kg=1.8082×1030kg

The reaction for which energy released is to be calculated is,

10e++10e200γ

The energy released is calculated by Einstein’s mass energy equation, that is,

ΔE=ΔmC2

Where,

• ΔE is the change in energy.
• Δm is the change in mass.
• C is the velocity of light.

Substitute the values of Δm and C in the equation.

ΔE=Δmc2ΔE=(1.8082×1030)(3×108)2ΔE=16

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