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Question
When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3λ, the stopping potential is `"V"/4`. If the threshold wavelength for the metallic surface is nλ. then value of n will be ______.
Options
7
8
9
10
Solution
When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3λ, the stopping potential is `"V"/4`. If the threshold wavelength for the metallic surface is nλ. then value of n will be 9.
Explanation:
Given: Case -1: For wavelength of incident radiation is λ, stopping potential is V,
Case -2: For wavelength of incident radiation is 3λ, stopping potential is `"V"/4`
Threshold wavelength for the metallic surface is λth = nλ.
To find: The value of n.
Let, Φo = `"hc"/lambda` be the work function for the metallic surface.
From Einstein's equation for photoelectric effect:
`"hc"/lambda=phi_o + "eV"` ...(i)
`"hc"/(3lambda)=phi_o + "e""V"/4` ... (ii)
From equations (i) and (ii):
`2/3"hc"/lambda = 3/4"eV"`
eV = `8/9"hc"/lambda` ...(iii)
Put value of eV from equation (iii) in equation (i).
`"hc"/lambda = "hc"/lambda_"th" + 8/9 "hc"/lambda`
λth = 9λ = nλ
n = 9
