Question

A certain metallic surface is illuminated with monochromatic light of wavelength, $\lambda$. The stopping potential for photo-electric current for this light is $3V_0$. If the same surface is illuminated with light of wave length $2\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photo- electric effect is :

• A. λ/6
• B. 6λ
• C. 4λ
• D. λ/4

Answer 1

The correct option is C

4λ

We have,

$\frac{hc}{\lambda }=W+e\left(3V_0\right)$ ….(1) where W is the work function and (3V₀) is the stopping potential when monochromatic light of wavelength l is used. Also,

$\frac{hc}{2\lambda }=W+e{V}_0$ ...(2)

is used. $\lambda$ where $V_0$ is the stopping potential when monochromatic light of wavelength $2\lambda$ Subtracting equation (2) from equation (1)

We get,

$\frac{hc}{2\lambda }=2e{V}_0$ ...(2)

$\therefore V_0=\frac{hc}{4e\lambda }$

Substituting in equation (2) we get,

$\frac{hc}{2\lambda }=W+e{V}_0=W+\frac{hc}{4\lambda }\therefore W=\frac{hc}{4\lambda }$

The threshold wavelength is therefore $4\lambda$ .