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  • 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.

Q: 11.32 (b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27\hspace{1mm}^{\circ}C ).  Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments. 

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Absolute temperature = 273+27=300K

Boltzmann's Constant=1.38\times10-23 J/mol/K

The de Broglie wavelength associated with the neutron is

\\\lambda =\frac{h}{p}\\ \lambda =\frac{h}{\sqrt{2m_{N}K}} \\\lambda =\frac{h}{\sqrt{3kT}}\\ \lambda =\frac{6.62\times 10^{-34}}{\sqrt{3\times 1.38\times 10^{-23}\times 300}}\\ \lambda =1.446 \dot{A}

Since this wavelength is comparable to the order of interatomic spacing of a crystal it can be used for diffraction experiments. The neutron beam is to be thermalised so that its de Broglie wavelength attains a value such that it becomes suitable for the crystal diffraction experiments.

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