From a metallic surface photoelectric emission is observed for frequencies v 1 and v 2 ( v 1 v 2 ) of the incident light. The maximum values of the kinetic energy of the photoelectrons emitt

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From a metallic surface photoelectric emission is observed for frequencies v 1 ​ and v 2 ​ ( v 1 ​ > v 2 ​ ) 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

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Using Einstein's photoelectric equation, ​ E k ​ = hv − ϕ 0 ​ E k ​ = hv − h v 0 ​ ∴ E K 1 ​ ​ = h ( v 1 ​ − v 0 ​ ) and E K 2 ​ ​ = h ( v 2 ​ − v 0 ​ ) Given E K 2 ​ ​ E K 1 ​ ​ ​ = x 1 ​ ⇒ v 2 ​ − v 0 ​ v 1 ​ − v 0 ​ ​ = x 1 ​ ( v 1 ​ − v 0 ​ ) x = v 2 ​ − v 0 ​ v 1 ​ x − v 0 ​ x = v 2 ​ − v 0 ​ ∴ v 1 ​ x − v 2 ​ = v 0 ​ x − v 0 ​ v 1 ​ x − v 2 ​ = v 0 ​ ( x − 1 ) ∴ v 0 ​ = x − 1 v 1 ​ x − v 2 ​ ​ ​

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