A narrow neutron beam falls on a natural face of an aluminium single-crystal at a glancing angle of `5^(@)` The distance between crystallographic planes parallel to the single-crystal face is 0.20 nm. What is the velocity and the energy of neutrons for which a first-order maximum is observed in this direction? What is the temperature responding to this neutron velocity?

Answer

`1.1xx10^(-19)J=0.68eV;1.1xx10^(4)m//s;5.4xx10^(3)K`

Explanation

Using the Bragg law for the first-order maximum (see 62.7), find the de Broglie wavelength for neutrons: `lamda=2dsinalpha`, where `alpha` is the glancing angle. From the wavelength we find the kinetic energy of neutrons their velocity and the corresponding temperature:
`K=h^(2)/(2mlamda^(2)),v=h/(mlamda),T=h^(2)/(3mklamda^(2))`