Physics Decay Problem?

Question

A neutron at rest undergoes decay, breaking up into a proton and an electron. This decay releases energy, which manifests as kinetic energy of the proton and electron. Given that the mass of a proton is approximately 1836 times that of an electron, what fraction of the total energy released is converted into the kinetic energy of the proton? Please express this fraction as K(p)/K(tot) = ____%.

Dr. Jacey Bergstrom IV · Accepted Answer

momentum is conserved so p=mv 
the kinetic energy is determined by the velocity
so take 
1/1836=5.44x10^-2 %
yes its right i already entered it

Anonymous · Answer

100/1836

Anonymous · Answer

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)/3672
Ke = (1/2)(me)(ve)^2 = (meve^2)/2
Kt = [(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 %

Anonymous · Answer

1/1836= 5.44*10^-4
This is the correct answer

Anonymous

Physics Decay Problem?

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