(a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn = 1.675 × 10–27 kg)(b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 °C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Asked by Saritha 14/10/2019 Last Modified 06/10/2025

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(a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn = 1.675 × 10–27 kg)(b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 °C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Asked by Saritha 14/10/2019 Last Modified 06/10/2025

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Harshit Bhardwaj · Accepted Answer

(a) De Broglie wavelength =; neutron is not suitable for the diffraction experiment
Kinetic energy of the neutron, K = 150 eV
= 150 &times; 1.6 &times; 10&minus;19
= 2.4 &times; 10&minus;17 J
Mass of a neutron, mn = 1.675 &times; 10&minus;27 kg
The kinetic energy of the neutron is given by the relation:

Where,
v = Velocity of the neutron
mnv = Momentum of the neutron
De-Broglie wavelength of the neutron is given as:

It is given in the previous problem that the inter-atomic spacing of a crystal is about 1 &Aring;, i.e., 10&minus;10 m. Hence, the inter-atomic spacing is about a hundred times greater. Hence, a neutron beam of energy 150 eV is not suitable for diffraction experiments.
(b) De Broglie wavelength = 
Room temperature, T = 27&deg;C = 27 + 273 = 300 K
The average kinetic energy of the neutron is given as:

Where,
k = Boltzmann constant = 1.38 &times; 10&minus;23 J mol&minus;1 K&minus;1
The wavelength of the neutron is given as:

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.

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