A certain metallic surface is illuminated by monochromatic radiation… | JEE Main 2021 (20 Jul, Shift 2)

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Photoelectric Effect: Einstein's Equation

A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$ . The stopping potential for photoelectric current for this radiation is 3V0. If the same surface is illuminated with a radiation of wavelength 2 $\lambda$ , the stopping potential is V0. The threshold wavelength of this surface for photoelectric effect is ____________ $\lambda$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 4

Einstein: $\frac{hc}{\lambda} = \phi + eV_s$ ; write $A = \frac{hc}{\lambda}$ .
$A - \phi = 3eV_0$ and $\frac{A}{2} - \phi = eV_0$
Subtract: $\frac{A}{2} = 2eV_0 \Rightarrow A = 4eV_0,\ \phi = eV_0 = \frac{A}{4}$
$\lambda_0 = \frac{hc}{\phi} = 4\lambda$
So the answer is 4, i.e. $\lambda_0 = 4\lambda$ .

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