A) \[{{10}^{-12}}cm\]
B) \[{{10}^{-10}}cm\]
C) \[{{10}^{-14}}cm\]
D) \[{{10}^{-15}}cm\,\]
Correct Answer: A
Solution :
[a] Distance of closest approach \[\text{Energy, }E=5\times {{10}^{6}}\times 1.6\times {{10}^{-19}}J.\] \[{{r}_{0}}=\frac{Ze\left( 2e \right)}{4\pi {{\varepsilon }_{0}}\left( \frac{1}{2}m{{v}^{2}} \right)}\] \[\therefore {{r}_{0}}=\frac{9\times {{10}^{9}}\times \left( 92\times 1.6\times {{10}^{-19}} \right)\times \left( 2\times 1.6\times {{10}^{-19}} \right)}{5\times {{10}^{6}}\times 1.6\times {{10}^{-19}}}\]\[\Rightarrow r=5.2\times {{10}^{-14}}m=5.3\times {{10}^{-12}}cm.\]
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