A) \[2\times {{10}^{-7}}s\]
B) \[4\times {{10}^{-8}}s\]
C) \[0.5\times {{10}^{-8}}\,s\]
D) \[3\times {{10}^{-6}}\,s\]
Correct Answer: B
Solution :
| The mean time between two collision \[\propto \frac{P}{\sqrt{T}}\] |
| \[\frac{\Delta {{t}_{1}}}{\Delta {{t}_{2}}}=\frac{{{P}_{1}}}{{{P}_{2}}}\times \frac{\sqrt{{{T}_{2}}}}{\sqrt{{{T}_{1}}}}\] |
| \[\Rightarrow \] \[\frac{6\times {{10}^{-8}}}{\Delta {{t}_{2}}}=\left( \frac{\sqrt{3}}{5} \right)\times 2\] |
| \[\Rightarrow \] \[\Delta {{t}_{2}}=6\times {{10}^{-8}}\times \frac{1}{2}\sqrt{\frac{5}{3}}\] |
| \[\approx 4\times {{10}^{-8}}\sec .\] |
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