An electron with angular momentum L moving around the nucleus has amagnetic moment given by(a) e L/ 2m (b) e L/3m (c) e L /4m (d) e L / m

To solve the problem, we need to derive the expression for the magnetic moment of an electron in terms of its angular momentum.

1. Break Down the Problem

We need to determine the relationship between the magnetic moment ($\mu$) and angular momentum ($L$) for an electron.

2. Relevant Concepts

The magnetic moment ($\mu$) of an electron in orbital motion is related to its angular momentum ($L$) by the formula: $\mu = \frac{e}{2m} L$ where $e$ is the charge of the electron and $m$ is its mass.

3. Analysis and Detail

In this case:

• $L$ is given,
• The electron has charge $e$ and mass $m$.

Using the formula: $\mu = \frac{e}{2m} L$

4. Verify and Summarize

From our derivation, we confirm that the magnetic moment can be expressed as a function of angular momentum. Given the options provided, we can see that the correct representation of the magnetic moment in relation to angular momentum is:

Final Answer

The magnetic moment is given by $\mu = \frac{eL}{2m}$, which corresponds to option (a) $eL/2m$.