$\begin{array}{1 1}(a)\;9.3\times 10^{15}Hz&(b)\;8.28\times 10^{16}Hz\\(c)\;7.32\times 10^{16}Hz&(d)\;8.13\times 10^{16}Hz\end{array}$

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Frequency = $\large\frac{1}{\text{Time period}}$

Time period = $\large\frac{\text{Total distance covered}}{\text{Velocity}}= \large\frac{2\pi r}{v}$

Frequency = $\large\frac{v}{2\pi r}$

The velocity $(v_2)$ and radius $(r_2)$ of the $2^{nd}$ Bohr's orbit :

$r_n=(0.53\times 10^{-10}n^2/z)m$

$r_2=(0.53\times 10^{-10}(2^2)m = 2.12\times 10^{-100}m$

$v_n=2.165\times 10^6(z/n)m/s$

$v_2=2.165\times 10^6(1/2)=1.082\times 10^6m/s$

Frequency=$\Large\frac{v_2}{2\pi r_2}=\frac{1.082\times 10^6}{2(\pi)(2.12\times 10^{-10})}$

$v=8.13\times 10^{16}Hz$

Hence (d) is the correct option.

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