Question

a) A nuclear reactor produces fast neutrons (with energy ∼ 1MeV) which are then slowed down to thermal neutrons (with energy of order E ∼ 0.025eV, comparable to their thermal energy at room temperature). In research reactors, both types of neutrons could be selected to exit through a port and used in scattering experiments to study crystals. Crystal lattice spacing is usually a few angstrom and to get information about the crystal in a scattering experiment the radiation wavelength should be on the same order of the lattice spacing. Would you select fast or thermal neutrons for a scattering experiment?

[Calculate the de Broglie wavelength in both cases to give a more quantitative answer.]

b) One of the largest object for which diffraction effects have been observed are buckyballs [see Nature 401, 680-682 (1999)], a molecule containing 60 Carbon atoms. In the experiment, the buckyball velocity was v ≈ 220m/s. What was the wavelength of the buckyball?

[Compare it to the diffraction grating used in the experiment consisting of 50-nm-wide slits with a 100-nm period. ]

Answer 1

(a) The moving neutrons will have both wave and particle character, of which the de Borglie wavelength of the particle should be comparable to the crystal lattice spacing, so that it can be used to get information about the crystal.

(Considering Non relativistic regime) We can write, the velocity of neutrons for Energy E as,

Therfefore for 1 MeV, we get velocity as,

The de Broglie wavelength is given as,

This is not in the order of Angstroms, so we will be using slow neutrons to study the crystal lattice.

(b) The de Broglie wavelength is given by,