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?

A narrow neutron beam falls on a natural face of an aluminium single-c

1.	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» SOLUTION :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))`

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