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  • When a metallic surface is illuminated with monochromatic light of wavelength  and stopping potential for p

When a metallic surface is illuminated with monochromatic light of wavelength \lambda and stopping potential for photoelectroc current is 3 \mathrm{~V}_0. When the same metallic surface is illuminated with a light of wavelength 2 \lambda, the stopping potentials is 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

Eistein’s photoelectric equation:

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

here \mathrm{W}= work function; and 

\frac{\mathrm{hc}}{2 \lambda}=\mathrm{e}\left(\mathrm{V}_0\right)+\mathrm{W}                        ...(2)

Solving these equations

(\mathrm{I})-3 \text { (II) }

\Rightarrow \quad \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 \quad \frac{\mathrm{hc}}{\lambda_0}=\frac{\mathrm{hc}}{4 \lambda}

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

 

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Anam Khan

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