Larmor precession: frequency shift in a magnetic field An electron orbits with angular frequency ω0 in the absence of a magnetic field. When a uniform magnetic field B is applied, the orbital frequency becomes approximately ω ≅ ω0 + (e / (2m)) * B, where e is the magnitude of electron charge and m its mass. Is this statement acceptable as written?

Introduction / Context:
In atomic physics, a weak magnetic field slightly modifies electron orbital motion, producing Larmor precession. This leads to a characteristic frequency shift of magnitude ωL = eB / (2m), central to magnetic resonance and Zeeman splitting concepts.

Given Data / Assumptions:

• Weak, uniform magnetic field B.
• Classical picture with small perturbation to an existing orbital frequency ω0.
• e denotes the positive magnitude of electron charge; sign conventions are handled in the direction of precession.

Concept / Approach:
The Larmor precession frequency for a charged particle of charge magnitude e and mass m in a magnetic field B is:

ωL = e * B / (2 * m).

The observed orbital frequency can be written as ω ≈ ω0 ± ωL; the sign depends on the sense of motion and charge sign. Using e as a positive magnitude, a compact way to state the shift is ω ≅ ω0 + (e / (2m)) * B, indicating an additive magnitude.

Step-by-Step Solution:
Identify the perturbative correction: ωL = eB / (2m).Combine with the unperturbed frequency: ω ≈ ω0 ± ωL.Accept the written form as representing a magnitude increase, with sign absorbed in precession direction conventions.

Verification / Alternative check:
Zeeman splitting energies are proportional to μB * B with μB = eħ / (2m); the same 1/2 factor appears consistently, reinforcing the Larmor frequency expression.

Why Other Options Are Wrong:
The factor eB/m (without 1/2) is incorrect for orbital Larmor precession. Saying frequency always decreases ignores sign conventions, and requiring time-varying B is unnecessary.

Common Pitfalls:
Confusing cyclotron frequency (eB/m for free translational motion) with Larmor precession (eB/2m for orbital angular momentum).

Final Answer:
True (using e as positive charge magnitude and indicating a frequency shift of magnitude eB/2m)