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 ______.

पर्याय

• 7

• 8

• 9

• 10

Answer 1

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 λ_th = nλ.

To find: The value of n.

Let, Φ_o = `"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`

λ_th = 9λ = nλ     

n = 9