Question

If Bohr's quantization postulate (angular momentum = `(n h)/(2 pi)`) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

Answer 1

Bohr’s quantization condition (L) = `(n h)/(2 pi)`

is a quantum mechanical effect that becomes significant only at atomic scales.

In atomic systems, masses are extremely small (electron mass), angular momentum is comparable to Planck’s constant h, and quantization becomes observable.

In planetary motion, masses are enormous (planet mass), and angular momentum is extremely large.

If we apply Bohr’s condition to a planet:

n = `(2 pi L)/h`

Since L ≫ h, the quantum number n becomes extremely large (of order 10⁷⁰ or more).

For very large quantum numbers, energy levels are extremely closely spaced, and orbits appear continuous rather than discrete. This corresponds to the classical limit (correspondence principle).

The spacing between successive quantized planetary orbits is so tiny that it is impossible to detect experimentally, and motion appears continuous and classical.

Bohr’s quantization is valid in principle for planetary motion, but the quantum effects are negligible because planck’s constant is extremely small and planetary angular momentum is extremely large. Hence, planetary orbits appear continuous and not quantized.