Q 12-12-058JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
An electron revolving in the $n^{\text{th}}$ Bohr orbit has magnetic moment $\mu_n$. If $\mu_n \propto n^x$, the value of $x$ is:
Answer: (B) $1$
$\mu = IA = \dfrac{ev}{2\pi r}\cdot\pi r^2 = \dfrac{evr}{2}$.
In the Bohr model $v \propto \dfrac1n$ and $r \propto n^2$, so $\mu \propto n$ (indeed $\mu = n\dfrac{e\hbar}{2m}$). Hence $x = 1$.
Solution by Sreeraj P, M.Sc Physics