A) \[\frac{{{e}^{2}}}{r}\]
B) \[\frac{{{e}^{2}}}{2r}\]
C) \[\frac{{{e}^{2}}}{r}\]
D) \[\frac{{{e}^{2}}}{2{{r}^{2}}}\]
Correct Answer: B
Solution :
\[\frac{m{{v}^{2}}n}{{{r}_{n}}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\left( \frac{z{{e}^{2}}}{{{r}^{2}}n} \right)=\frac{kz{{e}^{2}}}{{{r}^{2}}n}\] \[mv_{X}^{2}=\frac{z{{e}^{2}}}{{{r}_{v}}}\] Kinetic energy of electron in n an orbit \[KE=\frac{1}{2}mv_{n}^{2}=\frac{kz{{e}^{2}}}{2{{r}_{n}}}\] \[KE=\frac{{{e}^{2}}}{2r}\]
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