Bohr’s Quantization – Angular Momentum Condition (True/False) According to Bohr’s postulate for the hydrogen-like atom, only those circular orbits are stable for which the electron’s angular momentum equals an integer multiple of ħ (that is, L = n * h / (2π)). True or false?

Introduction / Context:
Bohr’s atomic model introduced the quantization of angular momentum to explain discrete spectral lines of hydrogen. Although superseded by full quantum mechanics, the postulate captures the essence of stationary orbits and energy quantization and remains a cornerstone in the historical development of atomic theory.

Given Data / Assumptions:

• Hydrogen-like atom, electron in a circular orbit.
• Bohr’s quantization condition postulated.
• Non-relativistic, old quantum theory context.

Concept / Approach:

Bohr postulated that only orbits satisfying L = nħ are permitted, where n is a positive integer, ħ = h/(2π). This leads directly to quantized radii and energies (En ∝ −1/n^2) and explains the Rydberg series. While modern quantum mechanics replaces “orbit” with stationary states, the allowed angular momenta still come in quantized units.

Step-by-Step Solution:

Verification / Alternative check:

Using Coulomb force balance plus the quantization condition reproduces hydrogen spectral lines via the Rydberg formula, confirming consistency of the postulate.

Why Other Options Are Wrong:

• False: contradicts the central Bohr assumption.
• Temperature or relativistic caveats are irrelevant to the original postulate’s validity within its model.

Common Pitfalls:

Equating Bohr orbits with exact quantum states in multi-electron atoms; overlooking that in quantum mechanics angular momentum quantization arises from boundary conditions on wavefunctions, not postulates about classical orbits.

Final Answer:

True