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Q.
According to Bohr model of hydrogen atom, the electric current due to motion of electron in $n^{th}$ orbit is proportional to
Atoms
Solution:
Electric current due to motion of electron in $n^{th}$ orbit is, $I_n = e\upsilon_n$
For hydrogen atom,
Frequency of electron in $n^{th}$ orbit is
$\upsilon_{n} = \left(\frac{1}{4\pi\varepsilon_{0}}\right)^{2} \frac{4\pi ^{2}e^{4} m}{n^{3}h^{3}}\quad\quad\dots\left(i\right)$
$\therefore \quad I_{n} = \left(\frac{1}{4\pi \varepsilon _{0}}\right)^{2} \frac{4\pi ^{2}e^{5} m}{n^{3}h^{3}}$ (Using $\left(i\right)$)
Thus, $I_{n} \propto \frac{1}{n^{3}}$