Dual Nature Of Light Question 106
Question: The ratio of de-Broglie wavelengths of molecules of hydrogen and helium which are at temperature $27^oC$ and $127^oC$ respectively is
Options:
A) $ \frac{1}{2} $
B) $ \sqrt{\frac{3}{8}} $
C) $ \sqrt{\frac{8}{3}} $
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
de-Broglie wavelength $ \lambda =\frac{h}{mv_{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 mv_{rms}=\sqrt{3,mk\ T} $ \ $ \lambda =\frac{h}{mv_{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}} $
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