Question

1. Gamma rays of energy Eγ are applied to protons that are stationary in the laboratory.

a) Calculate the momentum of gamma rays in the laboratory system.

b) Find the speed V of the center of gravity in the laboratory system.

c) What are the energies of gamma rays and protons in the center of gravity system?

Answer 1

since gamma rays are em waves,it has photons which does not have mass.so we can say that the energy of the radiation is equal to the momentum times velocity of light.therefore the momentum of the radiation is equal to

P = E/C where P is the momentum of the radiation , E is the energy of the radiation and C is the velocity of light which is 3*10^8 m/s

energy of a typical gamma ray can be lets say 8 mega-electron volts.so P =8*10^6*1.6*10^-19/3*10^8=4.27*10^-21 NS where I converted the electron volts into joules.

the mass of proton is 1.67*10^-27 kg,using momentum conservation ie assuming all he momentum is transfer to the proton ,we can find the velocity of the proton which is the center of mass of the system because em wave is a mass-less quantity by momentum conservation.

P =m*V

V=P/m where m is the mass of proton and P is the momentum of the radiation. V = 4.27*10^-27/(1.67*10^-27)=2.6 m/s

here i already assumed the energy of the gamma ray so the energy of the proton is ,.5mV^2=.5*1.27*10^-27*(2.6)^2=5.6*10^-27 joules