Question 17

An electron revolving in $$n^{th}$$ Bohr orbit has magnetic moment $$\mu_n$$. If $$\mu_n \propto n^x$$, the value of $$x$$ is:

Solution

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Magnetic moment of electron in $$n$$th Bohr orbit: $$\mu_n = \frac{eL}{2m_e}$$ where $$L = n\hbar$$ is the angular momentum.

$$\mu_n = \frac{en\hbar}{2m_e} \propto n$$

So $$\mu_n \propto n^1$$, meaning $$x = 1$$.

The correct answer is Option 2: 1.

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