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Question #43791

Difficulty: 8/10 | 🟢 Free

The Question

An electron (mass $m$ , charge $-e$ ) is initially in a circular Bohr orbit of a hydrogen-like atom. A weak uniform magnetic field $B$ is slowly turned on perpendicular to the orbital plane. Let $\Delta \omega_1$ be the actual change in the electron's angular velocity. A student calculates the change in angular velocity as $\Delta \omega_2$ by incorrectly assuming that the orbital angular momentum remains strictly quantized at its initial value $n\hbar$ even after the magnetic field is applied. What is the ratio $\frac{\Delta \omega_1}{\Delta \omega_2}$ ? (Ignore relativistic effects and electron spin).

Options

A.
$\frac{1}{4}$
B.
$\frac{1}{2}$
C.
2
D.
4

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Energy Level Scaling|Radius and Velocity Scaling|Angular Velocity vs Linear Velocity

Why This Question Is Tricky

Common Mistakes

This question tests the limits of the Bohr model and the application of the Bohr-Sommerfeld correspondence principle under perturbations.

A common trap is assuming that the orbital angular momentum remains strictly quantized ( $L = n\hbar$ ) when an external magnetic field is applied.

In reality, turning on the magnetic field induces an azimuthal electric field (Faraday's Law) that exerts a torque on the electron, changing its angular momentum.

By forcing students to compare the dynamic force balance ( $F_c = F_e + F_m$ ) with and without the correct angular momentum shift, the problem exposes the failure of static orbital stability and highlights the physical origin of Larmor precession.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Atoms - Class 12
Concept	Energy Level Scaling
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free