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) $e\left(3 V_{0}\right)=\frac{h c}{\lambda}-\phi_{0}\ldots$(i)
Case (ii) $e V_{0}=\frac{h c}{2 \lambda}-\phi_{0} \ldots$(ii)
From Eqs. (i) and (ii), we get
$\frac{3 h c}{2 \lambda}-3 \phi_{0}=\frac{h c}{\lambda}-\phi_{0}$
or $\frac{3 h c}{2 \lambda}-\frac{h c}{\lambda} =3 \phi_{0}-\phi_{0}$
$=\frac{h c}{2 \lambda}=2 \phi_{0} $
$ \Rightarrow \phi_{0} =\frac{h c}{4 \lambda} $
$\therefore $ Threshould frequency,
$\lambda_0 = \frac{hc}{\phi_0}$
$= \frac{hc}{hc} \times 4\lambda = 4\lambda$