(a) Obtain the de-Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in previous problem 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. Given `m_(n)=1.675xx10^(-27)kg`.
(b) Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature `(27^(@)C)`. Hence explain why a fast neutrons beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Explanation

To solve the problem, we will break it down into two parts as given in the question.

### Part (a): De-Broglie Wavelength of a Neutron

1. **Given Data**:
- Kinetic energy of the neutron (E) = 150 eV
- Mass of the neutron (m_n) = \(1.675 \times 10^{-27}\) kg
- Conversion factor: 1 eV = \(1.6 \times 10^{-19}\) Joules
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