Question

What is the de broglie wavelength of a nitrogen molecule in air at 300k?

Answer 1

Temperature of the nitrogen molecule, T = 300 K

Atomic mass of 'nitrogen' = 14.0076 u

Hence, mass of the nitrogen molecule, m = 2 × 14.0076 = 28.0152 u

But 1 u = 1.66 × 10−27 kg

∴m = 28.0152 ×1.66 × 10−27 kg

Planck’s constant, h = 6.63 × 10−34 Js

Boltzmann constant, k = 1.38 × 10−23 J K−1

We have the expression that relates mean kinetic energy of the nitrogen molecule with the root mean square speed as:

=6.63×10−34[3×28.0152×1.66×10−27×1.38×10−23×300]−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

=.028×10−9m