Question

A certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$. The stopping potential for photoelectric current for this light is $3V_0$. If the same surface is illuminated with light of wavelength $2\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photoelectric effect is $y\lambda$. Find $y$.

Answer 1

Answer: 4

$e{V}_s=E-\varphi \Rightarrow V_s=\frac{hc}{\lambda e}-\frac{hc}{{\lambda }_{0}e}$
Here, $3V_0=\frac{hc}{{\lambda }_e}-\frac{hc}{{\lambda }_{0}e}...(i)$
and $V_0=\frac{hc}{2\lambda e}-\frac{hc}{{\lambda }_{0}e}...(ii)$
Equation (i) $-3\times$ Equation (ii), we get
$\Rightarrow 0=-\frac{hc}{2\lambda e}+\frac{2hc}{{\lambda }_{0}e}$
$\Rightarrow {\lambda }_0=4\lambda$