Question

When wavelength of incident radiation on the metal surface is reduced from 'λ₁' to 'λ₂', the kinetic energy of emitted photoelectrons is tripled. The work function of the metal is ______.
(h = Planck's constant, c =velocity of light)

Options

• `"hc"/2 [(2lambda_2 - lambda_1)/(lambda_1lambda_2)]`

• `"hc"[(3lambda_2 - lambda_1)/(lambda_1lambda_2)]`

• `"hc"[(2lambda_2 - lambda_1)/(lambda_1lambda_2)]`

• `"hc"/2[(3lambda_2 - lambda_1)/(lambda_1lambda_2)]`

Answer 1

When wavelength of incident radiation on the metal surface is reduced from 'λ₁' to 'λ₂', the kinetic energy of emitted photoelectrons is tripled. The work function of the metal is `underline("hc"/2[(3lambda_2 - lambda_1)/(lambda_1lambda_2)])`.

Explanation:

E = `"hc"/lambda_1 - phi_0`

3E = `"hc"/lambda_2 - phi_0`

3E = `"3hc"/lambda_1 - 3phi_0`
-      -        +  

`0 = "hc"/lambda_2 - (3lambda"c")/lambda_1 + 3phi_0 - phi_0`

`(3lambda"c")/lambda_1 - "hc"/lambda_2 = 2phi_0`

`therefore phi_0 = "hc"/2[3/lambda_1 - 1/lambda_2]`

`= "hc"/2[(3lambda_2 - lambda_1)/(lambda_1lambda_2)]`