   Chapter 31, Problem 16PE

Chapter
Section
Textbook Problem

(a) What is the kinetic energy in MeV of a β ray that is traveling at 0.998c? This gives some idea of how energetic a β ray must be to travel at nearly the same speed as a γ ray. (b) What is the velocity of the ray relative to the β ray?

To determine

(a)

The kinetic energy of a β particle with a velocity 0.998c, in MeV

Explanation

Given:

From standard tables,

Rest mass of a β particle (electron)

m0=9.109×1031kg

Speed of the β particle

v=0.998c

Formula used:

The relativistic kinetic energy of a particle of rest mass m0is given by,

Ek=mm0c2

Here, m is the mass of the particle which moves with a velocity v, and is given by,

m=m01 v 2 c 2

Calculation:

Calculate the relativistic mass of the particle.

m=m01 v 2 c 2 =9.109×1031kg1 0.998c c 2=1

To determine

(b)

The velocity of a γ ray with respect to the βparticle.

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