Given :-
Mass of dust particle, m = 1 micro gram = 10^-6gm = 10^-9kg
Width of infinite potential well, a = 0.1 mm = 10^-4 m
Speed of dust particle, v = 10^-6 m /s.

We know that
E = (n² h²) / [8 m a²]
So, (1/2) m v² = (n² h²) / [8 m a²]
So, n² = [4 m² v² a²] / (h²)
So, n = (2 m v a) / h
So, n = [2 x (10^-9 kg) (10^-6 m/s) (10^-4 m)] / (6.6 x 10^-34 J.s)
So, n = 3 x 10¹⁴

Thus the quantum number associated with this motion is very large. So this result does not support the quantization of the energy.

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By :-   Dr. A. W. Pangantiwar