Question

# What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-mean square speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)

Solution

## Mass of $$N_2=2\times 14.0076u=28.0152\times 1.66\times 10^{-27}kg$$$$KE=3kT/2=mv_{rms}^2/2$$$$\Rightarrow v_{rms}=\sqrt{3kT/m}$$de-broglie wavelength is, $$h/mv_{rms}=0.028 nm$$.PhysicsNCERTStandard XII

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