Answer to Question #123277 in Atomic and Nuclear Physics for um-e-maheen

Question

Neutrons from a nuclear reactor are brought into thermal equilibrium by repeated collisions in heavy water at T = 300k. What is the average energy (in eV) and the typical wavelength of the neutrons ? Explain why they are diffracted when they pass through a crystalline solid.

Answer 1

If we have the equilibrium condition, then the energy of neutrons equal the energy of the medium where ones are.

Let E - energy of the neutrons, then

$E = ckT$

where : $k$ - Boltzmann constant

$T$ - the absolute temperature of the medium

$c$ - some constant

We want to get the average value of energy, so in this case we obtain the formula:

$E = kT$

Computation:

$E = 8.6173*10^{-5} \frac{eV}{K} * 300 K = 0.0258 eV$

We know that the energy of a quantum particle (neutron, for example) equals to:

$E = hv$ or $v=\frac{E}{h}$

where $h$ - Planck constant

$v$ - the frequency of the quant-wave

Computation:

$v = \frac{0.0258 eV}{4.1357e-15 eV*sec} = 6450*10^{9} Hz = 6450 MHz$

Why have neutrons diffracted with the molecules of the matter in nuclear reactor?

Well, it's easy to understand. We can consider the experiment: get the solid body, the source of the neutrons(with collimator of neutrons, of course) and the luminiscencne screen. If we send neutrons beam to a solid body, then we can to obtain the diffraction picture on the screen. We can think about diffraction like about probability collisions of neutrons with the atoms of solid body. The probability nature depends from the frequency of the quant. And if we have large frequency then we have small dispersion of the neutron beam and vice versa.