Dual Nature of Radiation and Matter - Result Question 23

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25. When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2 \lambda$, the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is :

======= ####25. When a metallic surface is illuminated with radiation of wavelength $\lambda$, the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2 \lambda$, the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is :

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(b) $5 \lambda$

(c) $\frac{5}{2} \lambda$

(d) $3 \lambda$

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Answer:

Correct Answer: 25. (d)

Solution:

  1. (d) According to Einstein’s photoelectric effect,

$eV=\frac{hc}{\lambda}-\frac{hc}{\lambda_0}$

$eV / 4=\frac{hc}{2 \lambda}-\frac{hc}{\lambda_0}$

Dividing equation (i) by (ii) by

$\Rightarrow 4=\frac{\frac{1}{\lambda}-\frac{1}{\lambda_0}}{\frac{1}{2 \lambda}-\frac{1}{\lambda_0}}$ on solving we get,

$\lambda_0=3 \lambda$

Threshold wavelength $(\lambda_0)$ is the maximum wavelength of incident radiations required to eject the electrons from a metallic surface.

If incident wavelength $\lambda>\lambda_0$

$\Rightarrow$ No photoelectron emission occur