A) \[4\times {{10}^{-8}}s\]
B) \[3\times {{10}^{-6}}s\]
C) \[0.5\times {{10}^{-8}}s\]
D) \[2\times {{10}^{-7}}s\]
Correct Answer: A
Solution :
| [a] Mean time between two successive collisions \[\tau \propto \frac{1}{\begin{align} & velocity\times number\text{ }ot\text{ }particles \\ & per\,unit\,volume \\ \end{align}}\] |
| \[\Rightarrow \]\[\tau \propto \frac{1}{\sqrt{T}}\frac{T}{P}=\frac{\sqrt{T}}{P}\therefore {{\tau }_{1}}={{\tau }_{2}}\frac{{{P}_{2}}}{{{P}_{1}}}\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] |
| \[\Rightarrow \]\[{{\tau }_{2}}=\frac{6\times {{10}^{-8}}}{2}\sqrt{\frac{500}{300}}=\sqrt{15}\times {{10}^{-8}}\simeq 4\times {{10}^{-8}}s\] |
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