Q: 11.19 What is the de Broglie wavelength of a nitrogen molecule in air at ? Assume that the molecule is moving with the root-mean-square speed of molecules at this temperature. (Atomic mass of nitrogen )
Since the molecule is moving with the root-mean-square speed the kinetic energy K will be given by
K=3/2 kT where k is the Boltzmann's constant and T is the absolute Temperature
In the given case Kinetic Energy of a Nitrogen molecule will be
Mass of Nitrogen molecule = 214.00761.6610-27=4.6510-26kg
The momentum of the molecule is
Associated De Broglie wavelength is
The nitrogen molecule will have a De Broglie wavelength of 0.0275 nm.