An electron revolving in nth  Bohr orbit has magnetic moment μn. If μnαnx, the value of x is:

1. Break Down the Problem

We need to find the value of $x$ in the expression for the magnetic moment $\mu_n$ of an electron in the $n$th Bohr orbit, given that $\mu_n \propto a_n x$, where $a_n$ is some function of $n$.

2. Relevant Concepts

The magnetic moment $\mu_n$ for an electron in the $n$th orbit is given by the formula: $\mu_n = \frac{e}{2m} L_n$ where $L_n$ is the angular momentum of the electron in the $n$th orbit, $e$ is the charge of the electron, and $m$ is the mass of the electron.

From Bohr’s model, the angular momentum $L_n$ of the electron can be expressed as: $L_n = n \hbar$ where $\hbar$ is the reduced Planck's constant.

Thus, we can express the magnetic moment as: $\mu_n = \frac{e}{2m} (n \hbar)$

3. Analysis and Detail

This can be rearranged to show the dependence on $n$: $\mu_n = \frac{e \hbar}{2m} n$ This shows that the magnetic moment $\mu_n$ is directly proportional to $n$.

4. Verify and Summarize

From the equation $\mu_n = k n$ where $k = \frac{e \hbar}{2m}$, we identify that $\mu_n$ indeed depends linearly on $n$.

Given $\mu_n \propto a_n x$ and now $\mu_n$ is proportional to $n$, we can deduce: $a_n \propto n \implies x = 1$

Final Answer

The value of $x$ is $1$.