In a hydrogen-like species, the net force acting on a revolving electron in an orbit as given by the Bohr model is proportional to $[n \to Principle quantum number, z \to atomic number]$

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$\frac{z^{2}}{m^{3}}$

$\frac{n^{3}}{z^{2}}$

$\frac{n^{4}}{z^{3}}$

$\frac{z^{3}}{n^{4}}$

answer is A.

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Detailed Solution

The net force on a revolving electron is $F = \frac{m v^{2}}{r}, F α \frac{v_{n}^{2}}{r_{n}}$

The velocity of the electron in the nth shell $V_{n} α \frac{z}{n}$ and The radius of the nth shell

$r_{n} α \frac{n^{2}}{z} \Rightarrow F α \frac{z^{3}}{n^{4}}$

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