A) \[{{n}_{0}}{{\alpha }^{1/4}}\]
B) \[{{n}_{0}}{{\alpha }^{-3}}\]
C) \[{{n}_{0}}{{\alpha }^{-3/4}}\]
D) \[\sqrt{{{n}_{0}}}{{\alpha }^{1/2}}\]
Correct Answer: C
Solution :
Given number density of molecules of gas as a function of r is\[n(r){{n}_{0}}{{e}^{-\alpha {{r}^{4}}}}\] \[\therefore \]Total number of molecule\[=\int\limits_{0}^{\infty }{n(r)}dV\] \[=\int\limits_{0}^{\infty }{{{n}_{0}}{{e}^{-\alpha {{r}^{4}}}}4\pi {{r}^{2}}}dr\] \[\therefore \]Number of molecules is proportional to\[{{n}_{0}}{{\alpha }^{-3/4}}\]
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