Physics - Modern Physics Question with Solution | TestHub

According to Einstein's equation for P.E.E.

For$1^{\mathrm{s}\mathrm{t}}$case,
$\frac{1}{2}{\mathrm{mv}}^2=\mathrm{hf}-\mathrm{W}$, where$\mathrm{f}=$frequency of incident light and$\mathrm{W}=$work function

For$2^{\mathrm{n}\mathrm{d}}$case,
$\frac{1}{2}{{\mathrm{mv}}_1}^2=\mathrm{h}\left(4\mathrm{f}\right)-\mathrm{W}$
$\frac{1}{2}{{\mathrm{mv}}_1}^2=4\mathrm{hf}-4\mathrm{W}+3\mathrm{W}$
$\frac{1}{2}{{\mathrm{mv}}_1}^2=4\left(\mathrm{hf}-\mathrm{W}\right)+3\mathrm{W}$
$\frac{1}{2}{{\mathrm{mv}}_1}^2=4\frac{1}{2}{\mathrm{mv}}^2+3\mathrm{W}$
$\frac{1}{2}{{\mathrm{mv}}_1}^2=\frac{1}{2}\mathrm{m}{\left(2\mathrm{v}\right)}^2+3\mathrm{W}$

This equation tells us on comparison that,
${\mathrm{v}}_1>2\mathrm{v}$