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Question: The ratio of de-Broglie wavelengths of molecules of hydrogen and helium which are at temperature 27 ...

The ratio of de-Broglie wavelengths of molecules of hydrogen and helium which are at temperature 27 ºC and 127 ºC respectively is –

A

12\frac{1}{2}

B

38\sqrt{\frac{3}{8}}

C

83\sqrt{\frac{8}{3}}

D

1

Answer

83\sqrt{\frac{8}{3}}

Explanation

Solution

l = h3(MwNA)kT\frac{h}{\sqrt{3\left( \frac{M_{w}}{N_{A}} \right)kT}} µ 1MwT\frac{1}{\sqrt{M_{w}T}}

λH2λHe\frac{\lambda_{H_{2}}}{\lambda_{He}} = MwHe×THeMwH2×TH2\sqrt{\frac{M_{w_{He}} \times T_{He}}{M_{w_{H_{2}}} \times T_{H_{2}}}}= 42×400300\sqrt{\frac{4}{2} \times \frac{400}{300}} = 83\sqrt{\frac{8}{3}}