Question

When a metallic surface is illuminated by a light of wavelength $\lambda$ the stopping potential for the photoelectric current is 3 V. When the same surface is illuminated by light of wavelength $2\lambda$ the stopping potential is 1 V. The threshold wavelength of this surface is

• A. $\lambda$
• B. $2\lambda$
• C. $3\lambda$
• D. $4\lambda$

Answer 1

The correct option is D $4\lambda$

For photo electric effect
$\frac{hc}{\lambda }=\frac{hc}{{\lambda }_0}+e{V}_s\Rightarrow \frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}=3eV...\left(1\right)\Rightarrow \frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}=eV...\left(2\right)\therefore \frac{1}{\lambda }-\frac{1}{{\lambda }_0}=3(\frac{1}{2\lambda }-\frac{1}{{\lambda }_0})\frac{3}{{\lambda }_0}-\frac{1}{{\lambda }_0}=\frac{3}{2\lambda }-\frac{1}{\lambda }\frac{2}{{\lambda }_0}=\frac{1}{2\lambda }\Rightarrow {\lambda }_0=4\lambda$