A) \[\sqrt{\frac{5}{3}}\]
B) \[\sqrt{\frac{8}{3}}\]
C) \[\sqrt{\frac{3}{8}}\]
D) \[\sqrt{\frac{3}{5}}\]
Correct Answer: B
Solution :
de-Broglei wavelength is,\[\lambda =\frac{h}{mv}\] From \[KTG,{{v}_{rms}}=\sqrt{\frac{3KT}{m}}\] where m is mass of gas molecule. So,\[\frac{{{\lambda }_{H}}}{{{\lambda }_{He}}}=\frac{{{m}_{He}}{{v}_{He}}}{{{m}_{H}}{{v}_{H}}}=\sqrt{\frac{{{m}_{He}}{{T}_{He}}}{{{m}_{H}}{{T}_{H}}}}\]\[=\sqrt{\frac{4\times 400}{2\times 300}}=\sqrt{\frac{8}{3}}\]
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