Question

When a surface 1 cm thick is illuminated by light of wavelength 'λ', the stopping potential is 'V₀'. When the same surface is illuminated by light of wavelength '3λ', the stopping potential is `"V"_0/6`. The threshold wavelength for the metallic surface is ______.

Options

• 3λ

• 2λ

• 4λ

• 5λ

Answer 1

When a surface 1 cm thick is illuminated by light of wavelength 'λ', the stopping potential is 'V₀'. When the same surface is illuminated by light of wavelength '3λ', the stopping potential is `"V"_0/6`. The threshold wavelength for the metallic surface is 5λ.

Explanation:

eV₀ = `"hc"/lambda - "hc"/lambda_0 = "hc"(1/lambda - 1/lambda_0)`   ...(1)

`("eV"_0)/6 = "hc"(1/(3lambda) - 1/lambda_0)`   ...(2)

Dividing Eq.(l) by Eq. (2) we get

6 = `((1/lambda - 1/lambda_0))/((1/(3lambda) - 1/lambda_0))`

Solving this equation for λ₀ we get λ₀ = 5λ