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Question #43018

Difficulty: 8/10 | 🟢 Free

The Question

Consider a hydrogen-like exotic atom consisting of a nucleus of mass $M$ and charge $+e$ , and a negatively charged particle of mass $m$ and charge $-e$ . The two particles orbit their common center of mass under mutual Coulombic attraction. If the system is in the $n^{\text{th}}$ Bohr quantized state (where the total orbital angular momentum of the system is $n\hbar$ ), what is the magnitude of the total orbital magnetic dipole moment of the atom? Assume $M > m$ .

Options

A.
$\frac{n e \hbar}{2} \left( \frac{1}{m} - \frac{1}{M} \right)$
B.
$\frac{n e \hbar}{2} \left( \frac{1}{m} + \frac{1}{M} \right)$
C.
$\frac{n e \hbar}{2m}$
D.
$\frac{n e \hbar}{2M}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Magnetic Field on Axis vs. Center|Magnetic Moment of Orbiting Electron|Reduced Mass Effect

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to transition from the classical infinite-nuclear-mass Bohr model to real two-body dynamics.

A common trap is for students to recognize that finite mass requires the use of reduced mass ( $\mu$ ), and then blindly substitute $m \to \mu$ into the standard Bohr magneton formula, yielding Option B.

Another trap is ignoring the nuclear motion entirely, yielding Option C.

The physical reality is that both particles orbit the center of mass in the same angular direction.

Because they have opposite charges, their equivalent current loops generate magnetic moments in opposite directions.

Therefore, the total magnetic moment is the difference between the two individual moments, not the sum, which fundamentally alters the standard quantization result.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Magnetic Field on Axis vs. Center
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free