   Chapter 31, Problem 15PE

Chapter
Section
Textbook Problem

What is the radio of the velocity of a 5.00−MeV (ray to that of an (panicle with the same kinetic energy? This should con?rm that (travel much faster than (s even when relativity is taken into consideration. (See also Exercise 31.11.)

To determine

The ratio of the velocity of a β particle to that of an a particle.

Explanation

Given info:

From standard tables,

Rest mass of a β particle (electron)  (m0)β=9.109×1031kg

Rest mass of an a particle  (m0)α=6.644×1027kg

The kinetic energy of the particles  Ek=5.00 MeV

Formula used:

The relativistic kinetic energy of a particle of rest mass m0 is given by,

Ek=(mm0)c2

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:

Express the kinetic energy in joules.

Ek=5.00 MeV×1.6× 10 13J1 MeV=8.00×1013J

Using the formula for relativistic kinetic energy, calculate the relativistic mass of the β particle using the values of rest mass and kinetic energy of the particle.

Ek=(mβ ( m 0 )β)c2mβ=Ekc2+( m 0)β

Using the given values,

mβ=Ekc2+( m 0)β=( 8.00× 10 13 J ( 3.00× 10 8 m/s ) 2 )+(9.109× 10 31kg)=9

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