Question

The given graphs show the variation of the stopping potential VS with the frequency (v) of the incident radiations for two different photosensitive materials M₁ and M₂. 

(i) What are the values of work functions for M₁ and M₂ ?

(ii) The values of the stopping potential for M₁ and M₂ for a frequency v₃ (>v₀₂) of the incident radiations are V₁ and V₂ respectively. Show that the slope of the lines equals V₁- V₂/V₀₂ -V₀₁.

Answer 1

(i) Work function of M₁ , W₁ = hv₀₁

Work function for M₂ , W₂ = hv₀₂

(ii) From Einstein’s potoelectric equation hv = W + eVs

VS = h/e v -W/e .......(1)

This is equation of a straight line of slope h/e.

From graph

For M₁ , hv₃ = hv₀₁ + eV₁ ...(2)

For M₂ , hv₃ = hv₀₂ + eV₂ ...(3)

Subtracting (2) from (3), we get

h(v₀₂ – v₀₁) + e (V₂ – V₁ ) = 0 

or h(v₀₂ – v₀₁) = e(V₁ – V₂ )

Slope of lines, h/e = V₁-V₂/V₀₂ -V₀₁