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  • when a centimeter thick surface is illuminated with a right of wavelength , the stopping potential is V. when th

when a centimeter thick surface is illuminated with a right of wavelength \lambda, the stopping potential is V. when the same surface is illuminated by light of wavelength 2\lambda the stopping potential is \mathrm{v / 3}. Threshold wavelength for the metallic surface is

Option: 1

\frac{4 \lambda}{3}


Option: 2

4 \lambda


Option: 3

6 \lambda


Option: 4

\frac{8 \lambda}{3}


Answers (1)

best_answer

 If stopping potential is\mathrm{ V_s}

\mathrm{\begin{aligned} & e V_S=h c\left(\frac{1}{\lambda}-\frac{1}{\lambda_0}\right)-(1) \\ & \frac{e V_S}{3}=h c\left(\frac{1}{2 \lambda}-\frac{1}{\lambda_0}\right)-(2) \end{aligned}}

 Dividing (1) \& (2) 

\mathrm{ \begin{aligned} & \Rightarrow 3=\frac{\frac{1}{\lambda}-\frac{1}{\lambda_0}}{\frac{1}{2 \lambda}-\frac{1}{\lambda_0}} \Rightarrow \frac{3}{2 \lambda}-\frac{3}{\lambda_0}=\frac{1}{\lambda}-\frac{1}{\lambda_0} \\ & \Rightarrow \frac{1}{2 \lambda}=\frac{2}{\lambda_0} \Rightarrow \lambda_0=4 \lambda . \end{aligned}}

 correct option is (B)

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vinayak

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