Question

When a certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$, the stopping potential for photoelectric current $3V_0$. When the same surface is illuminated with a light of wave length $2\lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface to photoelectric effect is

• A. $4\lambda$
• B. $6\lambda$
• C. $8\lambda$
• D. $\frac{4}{3}\lambda$

Answer 1

The correct option is A $4\lambda$

Given,

Wavelength of monochromatic light ${\lambda }_1=\lambda$

Stopping potential for photoelectric current $=3V_o$

Wavelength of second wave${\lambda }_2=2\times \lambda$

The stopping potential for the second photoelectric current $=V_o$,

Here, case (i) $e\left(3V_0\right)=\frac{bc}{\lambda }-{\varphi }_0$ ...(i)
Case (ii) $e{V}_0=\frac{bc}{2\lambda }-{\varphi }_0$ ...(ii)
From eqs. (i) and (ii),
$\frac{3bc}{2\lambda }-3{\varphi }_0=\frac{bc}{\lambda }-{\varphi }_0$
or $\frac{3bc}{2\lambda }-\frac{bc}{\lambda }=3{\varphi }_0-{\varphi }_0=\frac{bc}{2\lambda }=2{\varphi }_0$
or, ${\varphi }_0=\frac{bc}{4\lambda }$
$\therefore$ Threshold wavelength for this surface to photoelectric effect is
${\lambda }_0=\frac{bc}{{\varphi }_0}=\frac{bc}{bc}\times 4\lambda =4\lambda$