question_answer

The most probable kinetic energy of thermal neutrons at a temperature of T kelvin, may be taken as equal to kT, where k is Boltzmann constant. Taking the mass of a neutron and its associated de- Broglie wavelength as m and \[{{\lambda }_{B}}\] respectively, state the dependence of \[{{\lambda }_{B}}\] on m and T.

Answer:

                \[{{\lambda }_{B}}=\frac{h}{p}=\frac{h}{\sqrt{2mK}}=\frac{h}{\sqrt{2m\times kT}}\] \[\therefore \] \[{{\lambda }_{B}}\propto \frac{\mathbf{1}}{\sqrt{\mathbf{mT}}}\]