When a certain metallic surface is illuminated with monochromatic light of wavelength λ , the stopping potential for photoelectric current 3 V 0 . When the same surface is illuminated with a light o

Question

When a certain metallic surface is illuminated with monochromatic light of wavelength λ , the stopping potential for photoelectric current 3 V 0 ​ . When the same surface is illuminated with a light of wave length 2 λ , the stopping potential is V 0 ​ . The threshold wavelength for this surface to photoelectric effect is

TestHub · Accepted Answer

Here, case (i) e ( 3 V 0 ​ ) = λ hc ​ − ϕ 0 ​ Case (ii) eV 0 ​ = 2 λ hc ​ − From eqs. (i) and (ii), Fromeqs. (i) and (ii), 2 λ 3 h c ​ − 3 ϕ 0 ​ = λ h c ​ − ϕ 0 ​ or 2 λ 3 h c ​ − λ h c ​ = 3 ϕ 0 ​ − ϕ 0 ​ = 2 λ h c ​ = 2 ϕ 0 ​ or 2 λ 3 h c ​ − λ h c ​ or, ϕ 0 ​ = 4 λ h c ​ ∴ Threshold wavelength λ 0 ​ = ϕ 0 ​ hc ​ = hc hc ​ × 4 λ = 4 λ

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