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Question

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-broglie wavelength of nitrogen molecule is close to :
(Given : nitrogen molecule weight : 4.64×1026 kg, Boltzman constant : 1.38×1023 J/K, Planck constant :6.63×1034 J-s)

A
0.24 ˚A
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B
0.20 ˚A
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C
0.34 ˚A
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D
0.44 ˚A
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Solution

The correct option is A 0.24 ˚A
RMS speed of gas molecule,

Vrms=3kTm

de- Broglie wavelength, λ=hp=h2mK

λ=h2m×12mV2rms=hmVrms

λ=hm×3kTm=h3mkT

Substituting the respective values, we get

λ=6.63×10343×4.64×1026×1.38×1023×400=0.24 ˚A

Hence, option (A) is correct.

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