Question:
When the wavelength of radiation falling on a metal is changed from $500 \mathrm{~nm}$ to $200 \mathrm{~nm}$, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :
Correct Option: , 2
Solution:
(2)
Using equation, $=\frac{h c}{\lambda}-\phi$
$K E_{\max }=\frac{h c}{\lambda}-\phi=\frac{h c}{500}-\phi$ ....(1)
Again, $3 K E_{\max }=\frac{h c}{200}-\phi$ ....(2)
Dividing equation (2) by (1),
$\frac{3 K E_{\max }}{K E_{\max }}=\frac{3}{1}=\frac{\frac{h c}{200}-\phi}{\frac{h c}{500}-\phi}$
Putting the value of $h c=1237.5$ and solving we get, work function, $\phi=0.61 \mathrm{eV}$.