A) \[\frac{1}{2}\]
B) \[\sqrt{\frac{3}{8}}\]
C) \[\sqrt{\frac{8}{3}}\]
D) 1
Correct Answer: C
Solution :
de-Broglie wavelength \[\lambda =\frac{h}{m{{v}_{rms}}}\], rms velocity of a gas particle at the given temperature (T) is given as \[\frac{1}{2}mv_{rms}^{2}=\frac{3}{2}kT\]\[\Rightarrow {{v}_{rms}}=\sqrt{\frac{3\,kT}{m}}\]\[\Rightarrow m{{v}_{rms}}=\sqrt{3\,mk\ T}\] \ \[\lambda =\frac{h}{m{{v}_{rms}}}=\frac{h}{\sqrt{3\,mkT}}\] \[\Rightarrow \frac{{{\lambda }_{H}}}{{{\lambda }_{He}}}=\sqrt{\frac{{{m}_{He}}{{T}_{He}}}{{{m}_{H}}{{T}_{H}}}}=\sqrt{\frac{4\,(273+127)}{2\,(273+27)}}=\sqrt{\frac{8}{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
