A) 10 K
B) \[{{10}^{2}}K\]
C) \[{{10}^{3}}K\]
D) \[{{10}^{4}}K\]
Correct Answer: D
Solution :
The root mean square velocity of gas is \[{{\upsilon }_{rms}}=\sqrt{\frac{3kT}{m}}\] ?.(1) Escape velocity of gas molecules is \[{{\upsilon }_{es}}=\sqrt{2g{{R}_{e}}}\] As the root mean square velocity of gas molecules must be equal to the escape velocity \[\therefore \]From eqs. (1) and (2), we get \[\sqrt{\frac{3kT}{m}}=\sqrt{2g{{R}_{e}}}\] \[\Rightarrow \] \[T=\frac{2g{{R}_{e}}m}{3k}\] \[\Rightarrow \]\[T=\frac{2\times 9.8\times 6.4\times {{10}^{6}}\times 0.34\times {{10}^{-26}}}{3(1.38\times {{10}^{-23}})}\] \[={{10}^{12}}\] \[\therefore \] \[T={{10}^{3}}K\] \[=1000K\] Therefore,\[{{10}^{4}}K\]is the temperature at which hydrogen molecules will escape from earths surface.
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