A certain metallic surface is illuminated with monochromatic light of wavelength `lamda` . The stopping potential for photoelectric current for this light is `3V_0` . If the same surface is illuminated with light of wavelength `2 lamda` , the stopping potential is `V_0` . The threshold wavelength for this surface for photoelectric effect is

Options

A. `4lamda`
B. `lamda/4`
C. `lamda/6`
D. `6lamda`

Answer

A

Explanation

`k_("max") = (hc)/lamda -phi_0 ,V_0 = (hc)/(lamdae) - phi_0/e`
`:. 3V_0 = (hc)/lamda - (phi_0)/e " "...(i)`
and `V = (hc)/(2lamda) -phi_0 " "...(ii)`
From (i) and (ii)
`phi =(hc)/(4lamda)`
Now, threshold wavelength `lamda_0 = (hc)/phi`
`implies (hc)/(hc//4lamda)-4lamda`