K=10MeV=10×106×1.6×10−19J=1.6×10−12J
q1=2e=2×1.6×10−19C=3.2×10−19C - charge on alpha particle
q2=50e=50×1.6×10−19C=80×10−19C - charge on nucleus
The kinetic energy of the alpha particle must be converted to electrical potential energy at the point of closest approach.
We have: 21mv2=krq1q2
Distance of the closest approach is r=k21mv2q1q2
r=9×109×1.6×10−123.2×10−19×80×10−19=1.44×10−14 m
Answer: 1.44×10−14 m.
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