Q 12-11-127JEE MainJEE Main 2021 (20 Jul, Shift 2)Medium
A certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is $3V_0$. If the same surface is illuminated with a radiation of wavelength $2\lambda$, the stopping potential is $V_0$. The threshold wavelength of this surface for photoelectric effect is ______ $\lambda$.
Numerical value type. Enter your answer.
Answer: 4
$3eV_0 = \dfrac{hc}{\lambda} - \phi$ and $eV_0 = \dfrac{hc}{2\lambda} - \phi$.
Subtracting: $2eV_0 = \dfrac{hc}{2\lambda} \Rightarrow eV_0 = \dfrac{hc}{4\lambda}$. Then $\phi = \dfrac{hc}{2\lambda} - \dfrac{hc}{4\lambda} = \dfrac{hc}{4\lambda}$, so $\lambda_0 = \dfrac{hc}{\phi} = 4\lambda$.
Solution by Sreeraj P, M.Sc Physics