1. Magnetic moment of a revolving electron

   For an electron moving in a circular orbit, the magnetic moment is $\mu = I A$ where $I$ is the orbital current and $A$ is the area of the orbit.

2. Current due to revolving electron

   If the time period of revolution is $T$, then $I = \frac{e}{T}$ Also, for circular motion, $T = \frac{2\pi r}{v}$ Hence, $I = \frac{ev}{2\pi r}$

3. Area of the orbit

   $A = \pi r^2$

   Therefore, $\mu = IA = \frac{ev}{2\pi r} \cdot \pi r^2 = \frac{evr}{2}$

4. Use Bohr quantization

   In the Bohr model, $mvr = \frac{nh}{2\pi}$ So, $vr = \frac{nh}{2\pi m}$

   Substituting into magnetic moment: $\mu_n = \frac{e}{2}(vr) = \frac{e}{2}\cdot \frac{nh}{2\pi m}$ $\mu_n = \frac{neh}{4\pi m}$

   Thus, $\mu_n \propto n$

5. Compare with given form

   Since $\mu_n \propto n^x$ we get $x=1$

6. Option check

   • A: $2$ ❌
   • B: $0$ ❌
   • C: $3$ ❌
   • D: $1$ ✅

Therefore, the correct answer is D.