Radioactive beta decay is caused by the reaction n p + e + e, where n is the neu

Question

Radioactive beta decay is caused by the reaction n p + e + e, where n is the neutron, p is the proton, e is the electron, and e is the electron antineutrino. The mass of the neutron is 939.565 MeV/c^2, the mass of the proton is 938.272 MeV/c^2, the mass electron is 0.511MeV/c^2, and neutrinos are nearly mass- less. The mass change of the nucleon is (939.565938.272) MeV/c2 = 1.293 MeV/c^2, so the energy released is 1.293 MeV. If the elec- tron receives all of this energy, what is its velocity? Hint: Etot = mc2/ 1 (v/c)^2. Please answer this in a decimal in terms to speed of light.

Explanation / Answer

Etot = (mc2)/ (1 (v/c)2)

given that :

Etot = 1.293 MeV

m = 0.511MeV/c2

inserting the values

1.293 = (0.511)/ sqrt(1 (v/c)2)

v/c = 0.92

v = 0.92 c

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