Answer to Question #35592 in Atomic and Nuclear Physics for raogodavenkat

Question

compare momentum of 10^5eV X ray photon (Px) with that of a 10^5eV electron

Answer 1

momentum of photon is p= E/c = 10^5 eV/ (3*10^8 m/s^2) = 10^5 * 1.6 * 10^(-19) J / (3*10^8 m/s^2) = 5.33 * 10^(23) kg*m/s

Total energy of electron is sum of its kinetic energy and its rest energy, E=E_k+E_0

momentum of electron is (we will find exact relativistic value)
p=sqrt(E^2/c^2 - m^2 c^2) =sqrt((E_k+E_0)^2/c^2 - m^2 c^2) = sqrt(E_k^2+E_0)^2/c^2 - m^2 c^2) =

here we use that E_0^2/c^2
= m^2c^2 = sqrt(E_k^2+2E_kE_0)/c = sqrt(10^10 + 2*10^5*512*10^3)* 1.6 * 10^(-19) J /(3*10^8 m/s) =
1.79 * 10^(-22) kg*m/s

momentum of the electron of the same energy is bigger.