Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 ºC). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.
De Broglie wavelength = `1.447 xx 10^(-10) m`
Room temperature, T = 27°C = 27 + 273 = 300 K
The average kinetic energy of the neutron is given as:
`E = 3/2 kT`
k = Boltzmann constant = 1.38 × 10−23 J mol−1 K−1
The wavelength of the neutron is given as:
`lambda = h/sqrt(2m_n E) = h/(sqrt(3m_n KT))`
`= (6.6 xx 10^(-34))/sqrt(3xx1.675 xx 10^(-27) xx 1.38 xx 10^(-23) xx 300)`
`= 1.447 xx 10^(-10) m`
This wavelength is comparable to the inter-atomic spacing of a crystal. Hence, the high-energy neutron beam should first be thermalised, before using it for diffraction.