Electrons in Orbits under Magnetic Field Assertion (A): For an electron revolving in its atomic orbit, the presence of an external magnetic field alters its angular frequency. Reason (R): In that situation, the electron’s orbital magnetic dipole moment is not affected by the magnetic field.

Introduction / Context:
An orbiting charge behaves like a current loop and thus has an associated magnetic dipole moment. When an external magnetic field is applied, additional dynamics appear (classically the Larmor precession; quantum mechanically, Zeeman splitting). This question probes your grasp of how an external magnetic field modifies orbital motion and the resulting magnetic moment.

Given Data / Assumptions:

• Electron modeled as a charge moving in a bound orbit.
• Uniform external magnetic field is applied.
• Small-field (linear) response considered.

Concept / Approach:

The magnetic field exerts a Lorentz force on a moving electron, producing an additional torque that alters its angular motion. Classically, the electron’s orbital frequency acquires an increment known as the Larmor frequency, so the angular frequency is indeed affected. The orbital magnetic dipole moment μ is proportional to circulating current I and orbit area A: μ = I * A with I = qω/(2π). If ω changes, μ changes proportionally, so claiming that μ is unaffected is incorrect.

Step-by-Step Solution:

Verification / Alternative check:

Quantum picture: L · B coupling leads to Zeeman energy splitting ΔE = −μ · B; for weak fields the expectation value of μ relates to angular momentum and hence to the dynamical frequency character, reaffirming sensitivity to B.

Why Other Options Are Wrong:

• A and R both true: R is not true.
• A false but R true: contradicts standard Larmor/Zeeman results.

Common Pitfalls:

Assuming atomic orbit frequency is immutable; ignoring that any change in ω necessarily changes the current loop and its dipole moment.

Final Answer:

A is true but R is false