Finding the speed v of the proton

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SUMMARY

The discussion focuses on calculating the speed of a proton emitted from a nucleus using the principle of conservation of momentum. The initial momentum is zero due to the stationary nucleus, leading to the equation 0 = ((A-4) x a.m.u)(u) + (4 x a.m.u)(-v). The correct formula derived is v = (A/4 - 1)u, where A represents the mass number of the nucleus. The confusion arose from incorrectly subtracting 4 mass units, which pertains to alpha particle emission rather than a single proton emission.

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Homework Statement



image.jpg

Homework Equations


Principle of conservation of momentum,
Σpi=Σpf

The Attempt at a Solution


Since the nucleus is stationary, initial momentum is zero.
Unified atomic mass constant, a.m.u = 1.66 x 10^-27
Mass of the new nucleus: (A-4) x a.m.u
Mass of proton: 4 x a.m.u
0= ((A-4) x a.m.u )(u) + (4 x a.m.u )(-v)
4v = (A-4) u
v= (A/4 -1) u
So I chose A,
But the answer is B, where have I gone wrong?
 
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Why did you subtract 4 mass units from the atom when it only emitted a single proton? Were you thinking alpha particle?
 
gneill said:
Why did you subtract 4 mass units from the atom when it only emitted a single proton? Were you thinking alpha particle?
Oh yeah, I was. :nb)
thanks for the help :smile:
 

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