Question

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is:

• A. $\frac{2h}{\sqrt{mkT}}$
• B. $\frac{h}{\sqrt{mkT}}$
• C. $\frac{h}{\sqrt{3mkT}}$
• D. $\frac{2h}{\sqrt{3mkT}}$

Answer 1

The correct option is C $\frac{h}{\sqrt{3mkT}}$

At thermal equilibrium with heavy water

$E_k=\frac{3}{2}kT$

${\lambda }_D=\frac{h}{\sqrt{2E_{k}m}}\Rightarrow {\lambda }_D=\frac{h}{\sqrt{3mkT}}$