Question #107104
An α particle having energy 10Mev collides with a nucleus of atomic mass 50 . Then distance of closest approach will be ?
1
Expert's answer
2020-03-30T08:17:00-0400

K=10MeV=10×106×1.6×1019J=1.6×1012JK=10MeV=10\times 10^6 \times 1.6\times 10^{-19} J=1.6\times 10^{-12} J

q1=2e=2×1.6×1019C=3.2×1019Cq_1=2e=2\times 1.6\times 10^{-19} C=3.2\times 10^{-19}C - charge on alpha particle

q2=50e=50×1.6×1019C=80×1019Cq_2=50e=50\times 1.6\times 10^{-19} C=80\times 10^{-19}C - 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: 12mv2=kq1q2r\frac{1}{2}mv^2=k\frac{q_1 q_2}{r}

Distance of the closest approach is r=kq1q212mv2r=k\frac{q_1 q_2 }{\frac{1}{2}mv^2}

r=9×109×3.2×1019×80×10191.6×1012=1.44×1014 mr=9\times 10^9\times \frac{ 3.2\times 10^{-19}\times 80\times 10^{-19}}{1.6\times 10^{-12}}=1.44\times 10^{-14}\ m

Answer: 1.44×1014 m.1.44\times 10^{-14} \ m.


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