A free neutron undergoes decay with a half life of about 10.3 minutes and disint

Question

A free neutron undergoes decay with a half life of about 10.3 minutes and disintegrates to become a proton, an electron and an anti-electron neutrino as repressed by the reaction

n p+ + e + ¯ e

The masses of these particles are: mn = 1.00866 [u], mp+ = 1.00728 [u], me = 0.00055 [u], and m¯ e = 0. The mass of a neutrino is not in fact zero but it is quite small and has been very dicult to measure. The existence of neutrinos was established by carefully measuring the energy and momentum of the suite of particles emerging from decay - and in particular the fact that momentum was missing without taking neutrinos into account. Use the fact that 1 [u] = 931.5 MeV c2 to compute the combined kinetic energy of the decay products assuming that the neutron started at rest.

Explanation / Answer

E ( initial ) = E (rest neutron)

E( final) = E ( rest proton) + K ( proton) + E ( rest electron) + K ( electron) + E (neutrino) + K ( neutrino)

E ( final) = E ( rest proton) + E ( electron) + K ( all particles)----we have ignored the E of neutrion as it;s mass zero

K ( of all particles) = E ( rest neutron) - E ( rest proton) - E ( rest electron)

K =  931.5 MeV /c2 x 1.00866 -  931.5 MeV /c2 x 1.00728 - 931.5 MeV /c2 x 0.00055

K = 931.5 ( 0.00083) = 0.773145 Mev

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