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Chapter 37: Q. 26 (page 1082)

What is the total energy, in MeV, of

a. A proton traveling at 99% of the speed of light?

b. An electron traveling at 99% of the speed of light?

Hint: This problem uses relativity.

Short Answer

Expert verified

(a) Total energy for A proton traveling at 99% of the speed of light is6.66脳109eV.

(b) Total energy for An electron traveling at 99% of the speed of light is3.59脳106eV.

Step by step solution

01

Part (a) Step 1 Given Information :

A proton traveling at 99% of the speed of light .

We need to find the total energy in MeV.

02

Part (a) Step 2 Simplifation :

Mass of the proton is m=1.67脳10-27kg.

Velocity of the proton is v=0.99c.

Velocity of light cis c=3脳108

So energy is

E=mc21-v2/c2

=1.67脳10-27脳3脳10821-(0.99c)2/c2

=1.07脳10-9J

=6.66脳109eV.

03

Part (b) Step 1 Given Information :

An electron traveling at 99% of the speed of light .

We need to find the total energy in MeV.

04

Part (b) Step 2 Simplifation :

For an electron

Mass m=9.1脳10-31kg.

So the total energy is :

E=mc21-v2/c2

=9.1脳10-31脳3脳10821-(0.99c)2/c2

=5.74脳10-13J

=3.59脳106eV

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