First slide

Matter waves (DC Broglie waves)

Question

Find the ratio of de-Broglie wavelength of molecules of hydrogen and helium which are at temperature $27^{\circ} C and 127^{\circ} C$
respectively

Difficult

A

$\sqrt{5 / 3}$
B

$\sqrt{8 / 3}$
C

$\sqrt{3 / 5}$
D

$\sqrt{3 / 8}$

Solution

The de-Broglie wavelength is given by
$λ = \frac{h}{mv} We know that root mean square velocity ofa gas particles at a given temperature is given by \frac{1}{2} {mv}^{2} = \frac{3}{2} kT or V = \sqrt{(\frac{3 kT}{m})} or mv = \sqrt{3 mkT} Substituting the value ofmv from eq . (2) ill eq . (1), u . e get λ = \frac{h}{\sqrt{(3 mkT)}} So \frac{λ_{H}}{λ_{He}} = \sqrt{[\frac{m_{He} \cdot T_{He}}{m_{H} T_{H}}]} = \sqrt{\frac{(4) (273 + 127)}{(2) (273 + 27)}} = \sqrt{(\frac{8}{3})}$

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