Question

When a certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$, the stopping potential for photoelectric current is $3V_0$ and when the same surface is illuminated with light of wavelength $2\lambda$, the stopping potential is $V_0$. The threshold wavelength of this surface for photoelectric effect is $K\lambda$. Calculate the value of $K$.

Answer 1

$h\frac{c}{\lambda }=W+3e{V}_0$ ... (1)
$h\frac{c}{2\lambda }=W+e{V}_0$ ... (2)
$h\frac{c}{\lambda }[\frac{3}{2}-1]=2W$
$\frac{hc}{2\lambda }=2\frac{hc}{{\lambda }_0}$
${\lambda }_0=4\lambda$