Answer
The angular wave number $k$ is defined as
$k=\frac{2\pi}{\lambda}$
$\lambda$ can be expressed by the formula of de Broglie wavelength
$\lambda=\frac{h}{p}$
for a nonrelativistic particle, kinetic energy $K$ can be written as
$K=\frac{p^2}{2m}$
or, $p=\sqrt {2mK}$
Thus,
$\lambda=\frac{h}{\sqrt {2mK}}$
and therefore,
$k=\frac{2\pi}{\frac{h}{\sqrt {2mK}}}$
or, $k=\frac{2\pi\sqrt {2mK}}{h}$
Work Step by Step
The angular wave number $k$ is defined as
$k=\frac{2\pi}{\lambda}$
$\lambda$ can be expressed by the formula of de Broglie wavelength
$\lambda=\frac{h}{p}$
for a nonrelativistic particle, kinetic energy $K$ can be written as
$K=\frac{p^2}{2m}$
or, $p=\sqrt {2mK}$
Thus,
$\lambda=\frac{h}{\sqrt {2mK}}$
and therefore,
$k=\frac{2\pi}{\frac{h}{\sqrt {2mK}}}$
or, $k=\frac{2\pi\sqrt {2mK}}{h}$
