When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

0.61 eV

$ K_{max} = \frac{hc}{\lambda} - \phi $

For First case $K_1= \frac{1240}{500} - \phi = 2.48eV - \phi$

For Second case $K_1= \frac{1240}{200} - \phi = 6.2eV - \phi$

$\Rightarrow 6.2eV - \phi = 3(2.48eV - \phi) = 7.44eV - 3\phi$

$\Rightarrow 2\phi = 1.24eV $

$\Rightarrow \phi = 0.62eV$