Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature `(27^@C)`. Hence explain why a fast neutron beam needs to be thermalized with the environment before it can be used for neutron diffraction experiments.

Find the typical de-Broglie wavelength associated with a He atom in helium gas at room temperatuare (27^@C) and 1 atm pressure and compare it with the mean separation between two atoms under these conditions.

The de-Broglie wavelengths,associated with a proton and a neutron,are found to be equal.Which of the two has a higher value for kinetic energy?

Obtain the de-Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Q.NO.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 (m_n=1.675xx10^-27) .

Also find the de-Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of 3/2 KT at 300 K.

The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure structure of protons and neutrons appears at the minute length scale of 10^-15m or less. This structure was probed in early 1970's using high energy electron beams produced by a linear accelerator at stanford, USA. Guess what might have been the order of energy of these electrons beams. (Rest mass energy electron=0.511 MeV).

For what kinetic energy of a neutron will the associated de-Broglie wavelength be 1.40 xx 10^-10m ?

Find de-Broglie wavelength of neutron at 127 ^@C .Given,Boltzmann's constant k=1.38 xx 10^(-23) J mol^(-1) k^(-1) ,h = 6.625 xx 10^(-34) Js and mass of neutron = 1.66 xx 10^-27 kg .