The number density of molecules of a gas depends on their distance r from the origin as, n r = n 0 e - α r 4 . Then the numer of molecules is proportional to:

Step-by-step solution

Density of molecules of gas as a of r is, n ( r ) = n 0 e - α r 4 Total no. of molecules = ∫ 0 ∞ n ( r ) d v ∫ 0 ∞ n 0   e - α r 4 4 π r 2   d r To integrate this, substitute u = α 3 / 4 r 3   this will give us d r = 1 3 α 3 / 4 r 2 d u Now, the integration will become, 4 π n 0 3 α 3 / 4   ∫ 0 ∞   e - u 4 / 3 d u This shows that the numer of molecules is proportional to n 0 α - 3 / 4