Q. If a photon travels in an electric field(usually by a nucleus,such as ^12C),it can spontaneously disintegrate into an electron and a positron--known as pair production. A)Calculate the smallest possible photon frequency that produces pair production by assuming that both electron and positron are at rest. B)Calculate the momentum of the photon from A) C)Find the recoil velocity of the Carbon atom as a result of pair production. SOLUTION: i got the energy of the positron=energy of electron,so: E(e)=E(p)=mc^2=9.11×10^-31×(3×10^8) =8.2×10^-14 J = 0.511 MeV ⇒E of incident photon= E(e)+E(p)=1.04 MeV Finally,frequency will be:- f=E/h=2×8.2×10^-14/6.63×10^-34 =2.5×10^20 Hz and the momentum:- p=E/c=2×8.2×10^-14/3×10^8 =5.5×10^-22 kg.m/s Now, what i can't get is the recoil velocity of the carbon atom.I have no idea how, all i CAN get is the carbon atom's mass,which is: M=12×1.66×10^-27 ≈2.0×10^-26 kg. in the book the answer is 2.75*10^4 m/s. Pls Help!