The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number…
The force acting on the electron in hydrogen atom (Bohr' theory) is related to the principle quantum number ' $n$ ' as
$\mathrm{n}^4$
$\mathrm{n}^{-4}$
$\mathrm{n}^2$
$\mathrm{n}^{-2}$
Solution
The centripetal force of the rotating electron is given by $F=\frac{m^2}{r}$
But, according to Bohr, $\mathrm{v} \propto \frac{1}{\mathrm{n}}$ and $\mathrm{r} \propto \mathrm{n}^2$
i.e. $\mathrm{F} \propto \frac{\mathrm{v}^2}{\mathrm{r}^2}$
$\Rightarrow \mathrm{F} \propto \frac{1}{\mathrm{n}^2 \mathrm{n}^2}$
$\mathrm{F} \propto \frac{1}{\mathrm{n}^4}$