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Q.

Calculate the ratio of de-Broglie wavelength of molecules of hydrogen and oxygen kept in two separate jars at 27°C and 127°C respectively.

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a

$8 \sqrt{3}$

b

$\frac{8}{\sqrt{3}}$

c

$4 \sqrt{3}$

d

$\frac{\sqrt{3}}{2}$

answer is B.

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Detailed Solution

$\begin{array}{l} V_{rms} = \sqrt{\frac{3 RT}{M}} p = M V_{r m s} a n d λ = \frac{h}{p} = \frac{h}{\sqrt{\frac{3 RT}{M}} M} = \frac{h}{\sqrt{3 R T M}} \\ ∴ \frac{V_{H}}{V_{0}} = \sqrt{\frac{T_{H}}{M_{H}} \cdot \frac{M_{0}}{T_{0}}} = \sqrt{\frac{300}{2} \cdot \frac{32}{400}} = \sqrt{12} \\ \frac{λ_{H}}{λ_{0}} = \frac{h}{m_{H} V_{H}} \cdot \frac{m_{0} V_{0}}{h} = \frac{m_{0}}{m_{H}} \frac{V_{0}}{V_{H}} \\ = \frac{32}{2} \cdot \frac{1}{\sqrt{12}} = \frac{8}{\sqrt{3}} \end{array}$

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