Question

A certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$. The stopping potential for photoelectric current for this light is $3 V_{0}$. 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

$e V_{s}=E-\phi \Rightarrow V_{s}=\frac{h c}{\lambda e}-\frac{h c}{\lambda_{0} e}$
Here, $3 V_{0}=\frac{h c}{\lambda_{e}}-\frac{h c}{\lambda_{0} e}\,\,\,...(i)$
and $V_{0}=\frac{h c}{2 \lambda e}-\frac{h c}{\lambda_{0} e}\,\,\,...(ii)$
Equation (i) $-3 \times$ Equation (ii), we get
$\Rightarrow 0=-\frac{h c}{2 \lambda e}+\frac{2 h c}{\lambda_{0} e} $
$\Rightarrow \lambda_{0}=4 \lambda$