The frequency of revolution of the electron in Bohr's orbit varies with $n$, the principal quantum number as

The frequency of revolution of the electron in Bohr's orbit varies with $n$, the principal quantum number as
  1. $\frac{1}{n^4}$
  2. $\frac{1}{n^2}$
  3. $\frac{1}{\mathrm{n}}$
  4. $\frac{1}{n^3}$

Solution

$\begin{aligned} & f=\frac{v}{2 \pi r}=\left(\frac{V_0}{n}\right)\left(\frac{1}{2 \pi r_0 n^2}\right) \\ & f=\frac{V_0}{2 \pi r_0}=\left(\frac{1}{n^3}\right)=f_0\left(\frac{1}{n^3}\right)\end{aligned}$

Asked in: JEE Main 2025 (28 Jan Shift 2)

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