JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
The number density of molecules of a gas depends on their distance \(r\) from the origin as, \(n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}\). Then the total number of molecules is proportional to
- A \({n_0}{\alpha ^{ - 3/4}}\)
- B \({n_0}{\alpha ^{ - 3}}\)
- C \({n_0}{\alpha ^{ 1/4}}\)
- D \(\sqrt {{n_0}} {\alpha ^{1/2}}\)
Answer & Solution
Correct Answer
(A) \({n_0}{\alpha ^{ - 3/4}}\)
Step-by-step Solution
Detailed explanation
Given number density of molecules of gas as a function of \(r\) is \(n(r)=n_{0} e^{-a r^{4}}\) Total number of molecule \(=\int_{0}^{\infty} n(r) \mathrm{d} V=\int_{0}^{\infty} n_{0} e^{-\alpha x^{4}} 4 \pi r^{2} d r\) Number of molecules is proportional to…
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