Question

Stopping potentials of emitted photo electron is V when mono chromatic light of wavelength incident on a metal surface. If wavelength of light incident become 3 , stopping potential of photo electrons becomes V/4 then,the threshold wavelength of metal is k , then k will be :

Answer 1

Given : stopping potential = V when a mono chromatic light of wavelength λ incident on the metal surface.

wavelength of incident light becomes 3λ, stopping potential becomes V/4.

To find : if threshold wavelength of metal is kλ, then value of k will be...

solution : using photoelectric effect, hc/λ - hc/λ₀ = K.E_{max} = eV₀

case 1 : threshold wavelength λ₀ = kλ

stopping potential, V₀ = V

so, hc/λ - hc/kλ = eV ........(1)

case 2 : wavelength, λ = 3λ

stopping potential, V₀ = V/4

so, hc/3λ - hc/kλ = eV/4 .........(2)

dividing equations (1) by (2) we get,

(1/λ - 1/kλ)/(1/3λ - 1/kλ) = 1/(1/4)

⇒1/λ - 1/kλ = 4/3λ - 4/kλ

⇒3/kλ = 1/3λ

⇒k = 9

Therefore the value of k = 9