The Question is from neet-physics nuclei bohrs-model-of-atom, and it was created by the author P.NARASIMHA

Question

An electron moving around the nucleus with an angular momentum $l$ has a magnetic moment

P.NARASIMHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Relationship between magnetic moment and angular momentum of an electron.
	**Related Topics**: Bohr magneton, orbital magnetic moment, classical electromagnetism.
	**Prerequisites**: Understanding of angular momentum, magnetic moment, and basic properties of electrons.
## SOLUTION PATHWAY
**Given Information**:
	* Angular momentum of the electron: $l$
	* Electron charge: $e$
	* Electron mass: $m$
**Method & Steps**:
	1.  The magnetic moment (μ) of an electron due to its orbital motion is related to its angular momentum (l).
		Reasoning: The moving charge of the electron creates a current loop, which in turn generates a magnetic moment.
		Formula/Rule:  $\mu = \frac{e}{2m}l$
	2.  The magnetic moment is directly proportional to the angular momentum.
		Working: The proportionality constant involves the charge and mass of the electron.
	3.  Therefore, the magnetic moment is given by $\frac{e}{2m}l$.
		Result: $\mu = \frac{e}{2m}l$
		Verification: The units are consistent with magnetic moment.
 ## OPTION ANALYSIS
[A] :x: Incorrect proportionality constant.
[B] ✓: Correct relationship between magnetic moment and angular momentum for an electron.
[C] :x: Incorrect proportionality constant.
[D] :x: Incorrect proportionality constant and inclusion of $2\pi$.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing the formula with the Bohr magneton, which is specifically related to the angular momentum quantum number.
			[How to avoid]: Remember the general relationship between magnetic moment and angular momentum.
		2.[Error 2]: Incorrectly applying a factor of $2$ or $2\pi$.
			[How to avoid]: Carefully recall the derivation of the magnetic moment formula.
	**Quick Tips**:
		1.[Helpful shortcut]: Remember the gyromagnetic ratio is $\frac{e}{2m}$.
		2.[Memory aid]: Think of the electron's motion as a current loop, which generates a magnetic field and hence a moment proportional to the angular momentum.

P.NARASIMHA · Answer

$\frac{e}{m}l$

P.NARASIMHA · Answer

The correct Option is "$\frac{e}{{2m}}l$"

P.NARASIMHA · Answer

$\frac{{2e}}{m}l$

P.NARASIMHA · Answer

$\frac{e}{{2\pi m}}l$

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