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, $E_k=\frac{3}{2}kT$
momentum, $p=\sqrt{2m{E}_k}$
$p=\sqrt{2m\frac{3}{2}kT}$
and $\lambda =\frac{h}{p}$
$$\lambda =\frac{h}{\sqrt{3mkT}}$$