The magnetic moment (mu) of a revolving elect | vedclass

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(A) The magnetic moment $(\mu)$ of a revolving electron is given by the relation $\mu = \frac{e}{2m} L$,where $L$ is the angular momentum.According to

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$\mu \propto n$

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(A) The magnetic moment $(\mu)$ of a revolving electron is given by the relation $\mu = \frac{e}{2m} L$,where $L$ is the angular momentum.According to Bohr's quantization condition,the angular momentum $L$ of an electron in the $n$-th orbit is $L = \frac{nh}{2\pi}$.Substituting this value into the expression for magnetic moment,we get $\mu = \frac{e}{2m} \left( \frac{nh}{2\pi} \right)$.Rearranging the terms,we have $\mu = n \left( \frac{eh}{4\pi m} \right)$.Since $e$,$h$,and $m$ are constants,the term $\frac{eh}{4\pi m}$ is also a constant (related to the Bohr magneton $\mu_B = \frac{eh}{4\pi m}$).Therefore,$\mu \propto n$.

The magnetic moment $(\mu)$ of a revolving electron around the nucleus varies with principal quantum number $n$ as

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