A) n
B) \[\frac{{{n}^{3}}}{{{Z}^{2}}}\]
C) \[\frac{{{n}^{2}}}{Z}\]
D) \[\frac{Z}{n}\]
Correct Answer: B
Solution :
\[T=\frac{2\pi r}{v}\]; r = radius of nth orbit\[=\frac{{{n}^{2}}{{h}^{2}}}{\pi mZ{{e}^{2}}}\] v = speed of \[{{e}^{-}}\] in nth orbit \[=\frac{z{{e}^{2}}}{2{{\varepsilon }_{0}}nh}\] \ \[T=\frac{4\varepsilon _{0}^{2}{{n}^{3}}{{h}^{3}}}{m{{Z}^{2}}{{e}^{4}}}\] Þ \[T\propto \frac{{{n}^{3}}}{{{Z}^{2}}}\]
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