A proton (with a rest mass m=1.67×1027kg) has a total energy that is 4.00 times

Question

A proton (with a rest mass m=1.67×1027kg) has a total energy that is 4.00 times its rest energy.

Part A

What is the kinetic energy Ek of the proton?

Express your answer in billions of electron volts to three significant figures.

Ek= ????

Part B

What is the magnitude of the momentum p of the proton?

Express your answer in kilogram-meters per second to three significant figures.

p= ?????

Part C

What is the speed v of the proton?

Express your answer as a fraction of the speed of light to four significant figures.

v= ????

Explanation / Answer

a)

Given that

A proton with a rest mass m=1.67×1027kg

Total energy that is 4.00 times its rest energy.

Now the total energy Etotal =KE+mc2

KE =E-mc2

Then E =4mc2

Therefore KE =3mc2=3*(1.67×1027kg)(3*108m/s)2 =45.09*10-11J

We know that 1eV =1.6*10-19J

Then KE =28.18*108eV =2.818GeV

b)

The magnitude of the momentum p of the proton is given by

E2 =p2+c2+(mc2)2

E2 =(4mc2)2 =p2c2+m2c4

16m2c4-m2c4 =p2c2

p2 =15m2c2

P =1.940*10-18kg.m/s

c)

4mc2 =mc2/Sqrt(1- (v/c)2)

v2 =(15/16)c2

v =0.9682c

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