The number density of molecules of a gas depends on their distance from the origin as, n(r) = n₀e⁻αr⁴. Then the total number of molecules is proportional to:

Correct option is C. n₀α⁻³/₄
Given number density of molecules of gas as a function of r is
n(r) = n₀e⁻αr⁴
∴Total number of molecules = ∫₀^∞ n(r)dV = ∫₀^∞ n₀e⁻αr⁴ 4πr²dr
∴Number of molecules is proportional to n₀α⁻³/₄