Bohr model stability condition for hydrogen In a hydrogen atom, an electron orbits a proton. According to the Bohr (classical) picture, orbital stability requires equilibrium between the attractive Coulomb force and the required centripetal force. Is this statement correct?

Introduction / Context:
The Bohr model, though superseded by quantum mechanics, provides an intuitive picture of hydrogenic orbits. It relates electrostatic attraction to centripetal requirements for circular motion, combined with angular-momentum quantization, to explain discrete energy levels and spectral lines.

Given Data / Assumptions:

• Single electron moving in a circular orbit around a fixed proton.
• Non-relativistic speeds; classical Coulomb force law.
• Bohr quantization of angular momentum L = n h/(2π).

Concept / Approach:

For a circular orbit, the centripetal force m v^2 / r must be supplied by Coulomb attraction k e^2 / r^2 (with k = 1/(4π ε0), e the elementary charge). Equating these gives the relationship among m, v, and r. Combined with the angular momentum postulate, one solves for allowed radii r_n and energies E_n. This balance is the physical “stability” condition in the Bohr picture.

Step-by-Step Solution:

Verification / Alternative check:

In full quantum mechanics, the expectation values match Bohr predictions for hydrogen energy levels, validating the historical model’s results though not its orbital picture.

Why Other Options Are Wrong:

Limiting the validity to n = 1 or T = 0 is unnecessary in the Bohr framework; relativistic corrections are small and not required for the primary stability condition.

Common Pitfalls:

Confusing “stability” here with quantum stability; Bohr’s circular orbit analogy is a semi-classical construction leading to correct spectra despite its limitations.

Final Answer:

True