question archive A proton (with a rest mass m=1
A proton (with a rest mass m=1
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A proton (with a rest mass m=1.67×10−27kg) 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= ????
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a)
Given that
A proton with a rest mass m=1.67×10−27kg
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*(1.67×10−27kg)(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
