From a metallic surface photoelectric emission is observed for frequencies v₁ and v₂ (v₁>v₂ ) of the incident light. The maximum values of the kinetic energy of the photoelectrons emitted in the two cases are in the ratio 1: x . Hence the threshold frequency of the metallic surface is

Step-by-step solution

Using Einstein's photoelectric equation, aligned & E _ k = hv - ₀ & E _ k = hv - h v₀ & E _ K ₁ = h ( v ₁- v ₀ ) and E _ K ₂ = h ( v ₂- v ₀ ) & Given E_ K₁ E_ K₂ = 1 x & v₁-v₀ v₂-v₀ = 1 x & (v₁-v₀ ) x=v₂-v₀ & v₁ x-v₀ x=v₂-v₀ & v₁ x-v₂=v₀ x-v₀ & v₁ x-v₂=v₀(x-1) & v₀= v₁ x-v₂ x-1 & aligned