Question
Obtain the deBroglie wavelength associated with thermal neutrons at room temperature (27^{o} C). hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments. The mass of neutron is and the Boltzmann constant .

1.45 Å

1.25 Å

1.35 Å

None of these
medium
Solution
1.45 Å
The kinetic energy of a thermal neutron at absolute temperature T is given by
.
Here T = 27^{o} C = 300 K.
.
The deBroglie wavelength of these neutrons is given by
= 1.45 Å.
Thus, ‘thermal’ neutron have wavelength of the order of interatomic spacing and hence are suitable for diffraction experiments. Fast neutrons will possess wavelength quite small as compared to interatomic spacing and hence will not be suitable for diffraction experiments. Thus, for neutron diffraction experimants, fast neutron beam needs to be thermalised.
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