According to Bohr's model of hydrogen atom the electric current generated due to motion of electron in nth orbit is:

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$\begin{aligned} \frac{8 π^{2} m k^{2} e^{5}}{n^{3} h^{2}} \end{aligned}$

$\begin{matrix} \frac{16 π^{2} m k^{2} e^{4}}{n^{3} h^{2}} \end{matrix}$

$\frac{4 π^{2} m k^{2} e^{5}}{n^{3} h^{3}}$

$\frac{n^{2} h^{2}}{4 π^{2} m k^{2} e^{5}}$

answer is D.

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Detailed Solution

We know that;

$\begin{aligned} T_{n} = \frac{n^{3} h^{3}}{4 π^{2} k^{2} e^{4} \cdot m} \frac{1}{Z^{2}} \end{aligned}$

$i = \frac{q}{t} i = \frac{(e) \times m e \cdot e^{4} \times k^{2} \times 4 π^{2}}{h^{3} \cdot n^{3}}$

$i = \frac{4 π^{2} m k^{2} e^{5}}{n^{3} h^{3}}$

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