The threshold frequency of metal is f _ 0 . When the light of...

Maximum kinetic energy is related to the incident frequency $f$ and the threshold frequency ${f}_{0}$ as:

{K}_\max = hf - h{f}_{0}

When, $f = 2{f}_{0}$

$\dfrac{1}{2}m{v}_{1}^{2} = 2h{f}_{0} - h{f}_{0} = h{f}_{0} . . . \left(1\right)$

When, $f = 5{f}_{0}$

$\dfrac{1}{2}m{v}_{2}^{2} = 5h{f}_{0} - h{f}_{0} = 4h{f}_{0} . . . \left(2\right)$

Hence, the ratio, $\dfrac{{v}_{1}}{{v}_{2}} = \dfrac{1}{2}$