Radiation of wavelength λ is incident on a photocell. The fastest...

$\dfrac{1}{2}{mv}^{2} = \dfrac{hc}{\lambda} - ϕ$ ...(i)

$\dfrac{1}{2}mv{'}^{2} = \dfrac{4}{3}\dfrac{hc}{\lambda} - ϕ$ ...(ii)

From Eqn. (i)

$\dfrac{hc}{\lambda} = \dfrac{1}{2}{mv}^{2} + ϕ$

On putting this Equation (ii)

$\dfrac{1}{2}{mv}^{′2} = \dfrac{4}{3}\left(\dfrac{1}{2}{mv}^{2} + ϕ\right) - ϕ$

$v{'}^{2} = \dfrac{4}{3}{v}^{2} + \dfrac{2ϕ}{3m}$

$⇒ v ' > \sqrt{\dfrac{4}{3}}v$