Question

If Bohr quantisation postulates (angular momentum \[ = {\text{nh}}/2{{\pi }}\]) 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 quantisation of orbits of planets around the sun?

Answer 1

Hint: The higher is the value of angular momentum, more is the value of the energy shell and hence lesser will be the energy gap. This appears as continuous and not quantized.

Complete step by step solution:
The formula for angular momentum is \[\dfrac{{{\text{nh}}}}{{2{{\pi }}}}\]
Here n is the energy state and h is planck's constant. As we know that the mass of the planets is very - very large. The momentum is directly proportional to the mass of the object. This means earth and other planets must have very high momentum. The momentum of earth itself is in order of \[{10^{70}}{\text{ h}}\] which is a very large value. According to the formula of momentum, the momentum is directly proportional to n. Hence the earth having higher momentum will have higher n value. Now according to Bohr there is an inverse relationship between n and energy. This will make the energy difference between the energy states very low. Hence the energy states rather are continuous and not quantized. So quantization theory is not applicable to the planetary objects or motion.

Note:
Quantization refers to the definite set of orbits having fixed energy. The electrons present in the orbital have fixed energy and it neither loses or gains energy while moving in that particular level unless external energy is provided. Bohr’s model of an atom failed to explain the Zeeman Effect which is based on the magnetic field and stark effect which considers the electric field. It does not give account for spectra shown by species other than hydrogen and hydrogen like. It violates the Heisenberg uncertainty principle.