Following reactions are known as inverse beta decay
`p+vecvrarrn+e^(+)`
`n+vrarrp+e^(-)`
These reactions have extremely low probabilities. Because of this, neutrinos and antineutrinos are able to pass through vast amount of matter without any interaction. In an experiment to detect neutrinos, large number of neutrinos coming out from beta decays of a radioactive material were made to pass through a tank of water, containing a cadmium compound in solution, which provided the protons to interact with antineutrinos, which provided the protons to interact with antineutrinos. Immediately after a proton absorbed a neutrino to yield a positron and a neutron, the positron encountered an electron and both got annihilated. the gamma ray detectors surrounding the tanks responded to the resulting photons. This confirmed that the above reaction has taken place.
(a) How many gamma ray photons are produced when a electron annihilates with a positron? What is energy of each photon? Take the mass of an electron to be 0.00055 u.
(b) The neutron produced in the above reaction was captured by `.^(112)Cd` to form `.^(113)Cd`. The atomic masses of these two isotopes of cadmium are are 111.9028u and 112.9044u respectively. mass of a neutron is 1.0087u. find the Q value of this reaction. Assume half of this energy is excitation energ of `.^(113)Cd`. if the nucleus de-excites by emitting a gamma ray photon find its wavelenght.

Answer

(a) 0.51MeV (b) 6.60MeV,0.004 `overset(@)A`