Question

When a certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$, the stopping potential for photoelectric current 3$V_0$.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

Answer: (A)

Here, case (i) $e\left(3V_0\right)=\frac{hc}{\lambda }-{\varphi }_0\dots$(i)
Case (ii) $e{V}_0=\frac{hc}{2\lambda }-{\varphi }_0\dots$(ii)
From Eqs. (i) and (ii), we get
$\frac{3hc}{2\lambda }-3{\varphi }_0=\frac{hc}{\lambda }-{\varphi }_0$
or $\frac{3hc}{2\lambda }-\frac{hc}{\lambda }=3{\varphi }_0-{\varphi }_0$
$=\frac{hc}{2\lambda }=2{\varphi }_0$
$\Rightarrow {\varphi }_0=\frac{hc}{4\lambda }$
$\therefore$ Threshould frequency,
${\lambda }_0=\frac{hc}{{\varphi }_0}$
$=\frac{hc}{hc}\times 4\lambda =4\lambda$