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 :

Solution

Physics sir · 3 steps

Write Einstein's equation for both wavelengths, put in the factor of 3, and the work function drops out.

1. Photon energies. Use E = hc/λ with hc ≈ 1240 eV nm. At 500 nm, E₁ = 2.48 eV. At 200 nm, E₂ = 6.2 eV.
2. Einstein's equation. The maximum kinetic energy is K = E - φ. So K₁ = 2.48 - φ and K₂ = 6.2 - φ. The question says K₂ = 3K₁.

   6.2 - φ = 3(2.48 - φ) ⇒ 2φ = 7.44 - 6.2 = 1.24

3. So. φ = 0.62 eV. The closest option is (c) 0.61 eV.

The idea to keep. When a question gives a ratio of kinetic energies at two wavelengths, write K = hc/λ - φ for each one and solve the pair. Keep hc = 1240 eV nm ready.

Answer from the NTA final answer key. Solution by PrepWiser.