When a metallic surface is illuminated with monochromatic light of wavelength λ, stopping potential for photoelectric current is 3 V0. When the same metallic surface is illuminated with a light of wavelength 2λ, the stopping potential is V0. The threshold wavelength for the surface is-
Answer & explanation
Correct answer: option 2
$3V_0=\frac{hc}{eλ}-\frac{hc}{eλ_0}$ ...(1)
$V_0=\frac{hc}{2eλ}-\frac{hc}{eλ_0}$ ...(2)
$\frac{eq^n(1)}{eq^n(2)}⇒\frac{3V_0}{V_0}=\frac{\frac{hc}{eλ}-\frac{hc}{eλ_0}}{\frac{hc}{2eλ}-\frac{hc}{eλ_0}}$
$\frac{3}{2}\frac{hc}{eλ}-\frac{3hc}{eλ_0}=\frac{hc}{eλ}-\frac{hc}{eλ_0}$
$\frac{3}{2λ}-\frac{3}{λ_0}=\frac{1}{λ}-\frac{1}{λ_0}$
$\frac{2}{λ_0}=\frac{1}{2λ}$
$λ_0=4λ$