Dual Nature Of Radiation And Matter Ques 21
21. A certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$. The stopping potential for photo-electric current for this light is $3$ $ V_0$. If the same surface is illuminated with light of wavelength $2 \lambda$, the stopping potential is $V_0$. The threshold wavelength for this surface for photo-electric effect is
[2015]
(a) $4 \lambda$
(b) $\frac{\lambda}{4}$
(c) $\frac{\lambda}{6}$
(d) $6 \lambda$
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Answer:
Correct Answer: 21.(a)
Solution:
- (a) As we know,
$eV_s=\frac{hc}{\lambda}-\Psi$
$3 eV_o=\frac{hc}{\lambda}-\Psi$$\quad$ …….(1)
$eV_o=\frac{hc}{2 \lambda}-\Psi$$\quad$ …….(2)
$3 eV_o=\frac{3 hc}{2 \lambda}-3 \Psi$$\quad$ …….(3)
Multiplying eqn. (2) by (3) and subtracting it from eqn (1)
$\Psi=\frac{hc}{4 \lambda}$
So, threshold wavelength,
$\lambda _{\text{th }}=\frac{hc}{\Psi}=\frac{hc}{hc / 4 \lambda}=4 \lambda$
BETA
