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

• A. $6\lambda$
• B. $4\lambda /3$
• C. $4\lambda$
• D. $8\lambda$

Answer 1

Answer: (C)

$4\lambda$

Let threshold wavelength be ${\lambda }_0$

Therefore work function for the surface will be $W=\frac{hc}{{\lambda }_0}$

Stopping potential $V=\frac{E-W}{e}$ where $E$ is the energy of the incident beam ($\frac{hc}{\lambda }$) and $e$ is the charge on an electron.
Given

$3e{V}_0=\frac{hc}{\lambda }-\frac{hc}{{\lambda }_0}$

$e{V}_0=\frac{hc}{2\lambda }-\frac{hc}{{\lambda }_0}$

Multiplying the second eqaution by 3 and subtracting it from the first we get

$\frac{2hc}{{\lambda }_0}-\frac{hc}{2\lambda }=0$

Solving we get ${\lambda }_0=4\lambda$