The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum…
The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number 'n' as
- $n^{-2}$
- $n^{4}$
- $n^{-4}$
- $n^{2}$
Solution
Now $\begin{aligned} & F=\frac{m v^{2}}{r} \\ & v \propto \frac{1}{n} \text { and } r \propto n^{2} \\ & F \propto \frac{1}{n^{2}} \times \frac{1}{n^{2}} \\ F & \propto n^{-4} \end{aligned}$
$\therefore \quad \mathrm{F} \propto \frac{1}{\mathrm{n}^{2}} \times \frac{1}{\mathrm{n}^{2}}$
$\therefore \quad \mathrm{F} \propto \mathrm{n}^{-4}$
Asked in: MHT CET 2020 (16 Oct Shift 1)
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