When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

Calculation:
Let the work function of the metal be φ, and let the initial wavelength be λ₁ = 500 nm and the final wavelength be λ₂ = 200 nm. The energy of the photon is given by:

E = h× c / λ

where:

• h = Planck's constant
• c = speed of light
• λ = wavelength

Initially, the kinetic energy of the photoelectron is:

K.E. = E1 - φ = h × c / λ1 - φ

Finally, the kinetic energy becomes three times larger:

3 × K.E. = E2 - φ = h × c / λ2 - φ

From the ratio of the kinetic energies:

3 × (h × c / λ1 - φ) = h × c / λ2 - φ

Solve for φ (work function of the metal):

φ ≈ 0.61 eV

The correct answer is: 0.61 eV