Question

When a certain metallic surface is illuminated with monochromatic light of wavelength '`lambda`', the stopping potential for photoelectric effect is '3V₀'. If the same surface is illuminated with a light of wavelength '`2 lambda`', the stopping potential is found as 'V₀'. The threshold wavelength for this surface is ____________.

Options

• `lambda/4`

• `lambda/6`

• `6 lambda`

• `4 lambda`

Answer 1

When a certain metallic surface is illuminated with monochromatic light of wavelength '`lambda`', the stopping potential for photoelectric effect is '3V₀'. If the same surface is illuminated with a light of wavelength '`2 lambda`', the stopping potential is found as 'V₀'. The threshold wavelength for this surface is `4 lambda`.

Explanation:

`3 "V"_0 = "h" "c"/lambda - "h" "c"/lambda_0 = "hc" [1/lambda - 1/lambda_0]`

`"V"_0 = "hc"/(2lambda) - "hc"/lamda_0 ="hc" [1/(2lamda) - 1/lambda_0]`

`3"V"_0 = 3"hc" [1/(2lambda) - 1/lambda_0]`

`therefore 3"hc" [1/(2lambda) - 1/lambda_0] ="hc" [1/lambda- 1/lambda_0]`

`3/(2lambda) - 3/lamda_0 = 1/lambda - 1/lambda_0`

`3/(2lambda) - 1/lambda = 3/lambda_0 - 1/lambda_0 = 2/lambda_0`

`(3-2)/(2 lambda) = 2/lambda_0`

`lambda_0 = 4 lambda`