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Chapter 6: Q33E (page 1249)

A proton (rest mass 1.67脳10-27kg) has total energy that is 4.00 times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?

Short Answer

Expert verified

a)The kinetic energy of proton isK=4.5*10-10J

b)The magnitude of momentum of proton is 1.94*10-19kg/s

c)The speed of proton is v=0.968c

Step by step solution

01

Step 1:Formula for lorentz factor (γ),Kinetic energy(K) and total energy of a particle.

Lorentz factor,

纬=11-v2/c2

Kinetic energy,

K=mc21-v2/c2-mc2K=(纬-1)mc2

Total energy of a particle,

E=K+mc2

E2=(mc2)2+(Pc)2=16m2c4 where P is the magnitude.

02

Step 2:Calculating the kinetic energy of proton.

Given the mass of proton as1.67*10-27kg and total energy as 4times the rest energy.

Therefore the kinetic energy is,

E=mc2+K=mc2K=3mc2=3*(1.67*10-27kg)(3*108m/s)2=4.5*10-10J

03

Step 3:Calculating the magnitude of momentum of proton.

E2=(mc2)2+(Pc)2=16m2c415m2c4=P2c2P=15m2c2=15*mc=1.94*10-18kg.m/s

04

Step 4:Calculating the speed of the proton.

E=-mc21-v2/c1=4mc2116=1-v2c2v=c1516=0.968c

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