1. In the Bohr model, for the $n$th orbit of hydrogen-like atom:

   $r_n \propto n^2$

   and the electron speed varies as

   $v_n \propto \frac{1}{n}$

2. The frequency of revolution is

   $f_n = \frac{\text{speed}}{\text{circumference}} = \frac{v_n}{2\pi r_n}$

3. Substitute the dependences on $n$:

   $f_n \propto \frac{1/n}{n^2} = \frac{1}{n^3}$

4. Therefore, the frequency of revolution varies as

   $f_n \propto \frac{1}{n^3}$

5. Checking options:

   • A: $\frac{1}{n^4}$ ❌
   • B: $\frac{1}{n^2}$ ❌
   • C: $\frac{1}{n^3}$ ✅
   • D: $\frac{1}{n}$ ❌

Hence, the correct answer is Option C.