Question

If Bohr's quantization postulate \(\left(L=\dfrac{nh}{2\pi}\right)\) 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

Why Quantization is not Observed for Planetary Motion Concept: Bohr's quantization condition is \[ L=\frac{nh}{2\pi}, \] where \(n\) is an integer. Although this relation is a fundamental law, its observable consequences depend on the magnitude of the angular momentum involved.

Step 1: Compare atomic and planetary angular momenta. For an electron in an atom, the angular momentum is extremely small and comparable to \[ \frac{h}{2\pi}. \] Hence, the difference between successive allowed angular momentum values is significant and observable.

Step 2: Consider a planet revolving around the Sun. The angular momentum of a planet is enormously large. For example, \[ L_{\text{planet}} \gg \frac{h}{2\pi}. \] Consequently, the quantum number \(n\) becomes extremely large.

Step 3: Examine spacing between adjacent states. The difference between two successive allowed angular momentum values is \[ \Delta L = \frac{h}{2\pi}. \] Compared to the huge angular momentum of a planet, this difference is negligibly small. Therefore, adjacent quantized states are so closely spaced that they appear continuous.

Step 4: Physical implication. Because the allowed states are extremely close together, no measurable quantization effects can be detected in planetary motion. Hence, planetary orbits appear continuous rather than discrete. Conclusion: Bohr's quantization condition remains valid in principle, but for planets the quantum number is enormously large and the separation between adjacent quantized states is negligibly small. Therefore, planetary motion behaves classically and quantization is not observed experimentally. \[ \boxed{ \text{Planetary orbits appear continuous because their quantum numbers are extremely large.} } \]