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A mono-chromatic point source S radiating wavelength $\mathrm{6000 \AA}$ with power $2 \mathrm{w}_1$ an aperture A of diameter 0.1 metre and a large screen Sc are placed as shown in figure. A photo emission detector D of surface Area $0.5 \mathrm{~cm}^2$ is placed at the centre of the screen. The efficiency of the detector for the photo-electro generation per incident photon is 0.9

Question:

When a metallic surface is illuminated with monochromatic light of wavelength $\lambda$ the stopping potential for photoelectric current is $3 \mathrm{~V}_0$ . When the same metallic surface is illuminated with a light of wavelength $2\lambda$ , the stopping potential is $\mathrm{~V}_0$ . The threshold wavelength for the surface is
Option: 1
$6 \lambda$

Option: 2
$4 \lambda$

Option: 3
$4 \lambda / 3$

Option: 4
$8 \lambda$

Answers (1)

best_answer

Einstein’s photoelectric equation:

$\mathrm{\frac{\mathrm{hc}}{\lambda}=\mathrm{e}\left(3 \mathrm{~V}_0\right)+\mathrm{W}}$ [1]

here W = work function;

$\mathrm{\text { and } \frac{\mathrm{hc}}{2 \lambda}=\mathrm{e}\left(\mathrm{V}_0\right)+\mathrm{W}}$ [2]

Solving these equations

$\mathrm{\begin{aligned} & \Rightarrow \frac{\mathrm{hc}}{\lambda}=\frac{3 \mathrm{hc}}{2 \lambda}+\mathrm{W}-3 \mathrm{~W} \\ & \Rightarrow 2 \mathrm{~W}=\frac{\mathrm{hc}}{2 \lambda} \\ & \Rightarrow \frac{\mathrm{hc}}{\lambda_0}=\frac{\mathrm{hc}}{4 \lambda} \end{aligned}}$

$\mathrm{\Rightarrow \lambda_0=4 \lambda \quad \text { when } \lambda_0=\text { threshold wavelength }}$

Hence (B) is correct.

Posted by

Ritika Jonwal

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