Explanation:
Given, \(K=\) kinetic energy, \(m=\) mass
Then, \(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,K = \frac{1}{2}m{v^2}{\rm{ }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\)
But we know that, \(\lambda = \frac{h}{{mv}}{\rm{ }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( 2 \right)\)
Now, from Eq. (1), \({v^2} = \frac{{2K}}{m}\)
\( \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,v = \sqrt {2K/m} \)
Putting this in Eq. (2), we get
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{h}{{\sqrt {2mK} }}\)