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Physics Decay Problem?

A neutron at rest decays (breaks up) to a proton and an electron. Energy is released in the decay and appears as kinetic energy of the proton and electron. The mass of a proton is 1836 times the mass of an electron.What fraction of the total energy released goes into the kinetic energy of the proton?K(p)/K(tot)=____%
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4 Answers

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Everardo Feil

Feb 20, 2025

momentum is conserved so p=mv the kinetic energy is determined by the velocityso take 1/1836=5.44x10^-2 %yes its right i already entered it... Show More
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E
Everardo Feil

Feb 20, 2025

The other answers are close but they reach an (almost) correct result through wrong steps.First use conservation of momentum to find the velocity of the proton (vp) in terms of the velocity of the electron (ve) :(me = mass of electron, mp = mass of proton)-(me)(ve) = (mp)(vp)-(me)(ve) = (1836)(vp)vp = (-ve/1836)Now use kinetic energy equation to find energy of proton and divide by the total energy:(Kp = energy of proton, Ke = energy of electron, Kt = total energy)Kp = (1/2)(1836me)(-ve/1836)^2 = (meve^2)/3672Ke = (1/2)(me)(ve)^2 = (meve^2)/2Kt = [(meve^2)/3672] + [(meve^2)/2] = ((1837)(me)(ve^2)/3672)Now, we divide Kp by Kt and all of our terms cancel, leaving us with(1/1837) = 5.44x10^-2 %... Show More
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