Question

when wavelength of light incident on a metal surface changes from 500nm to 200nm, maximum possible kinetic energy of emitted photoelectrons become three times then find the work function of metal​

Answer 1

when wavelength of light incident on a metal surface changes from 500nm to 200nm, maximum possible kinetic energy of emitted photoelectrons become three times.

To find : the work function of metal.

solution : from photoelectric effect,

hc/λ - Φ = K.E_{max}

case 1 : wavelength of incident light, λ = 500 nm

let maximum kinetic energy is K.E

so, hc/(500 nm) - Φ = K.E ........(1)

case 2 : wavelength of incident light, λ = 200 nm

and maximum kinetic energy , K.E' = 3K.E

so, hc/(200nm) - Φ = 3 K.E ......(2)

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

[hc/(500nm) - Φ]/[hc/(200nm) - Φ] = 1/3

⇒3[hc/(500nm) - Φ] = [hc/(200nm) - Φ]

⇒3hc/(500nm) - 3Φ = hc/(200nm) - Φ

⇒3hc/(500nm) - hc/(200nm) = 2Φ

putting, hc = 1240 eV nm

so, 3(1240)/500 - 1240/200 = 2Φ

⇒-1.24 = 2Φ

⇒Φ = 0.62 eV ( this is approximately value of 0.61 eV which is given in option)

Therefore the correct option is (1) 0.61 eV