What is the work function of the metal if the light of wavelength 4000λ generates photo electrons of velocity 6 × 10^5 ms^-1 from it?

2.1 eV

4.0 eV

3.1 eV

None of these

To find the work function, we need to calculate the energy of the photon (E) and the kinetic energy of the electron (KE), then use the equation:

φ = E - KE

E = hc / λ = 1240 eV nm / 4000 nm = 3.1 eV

KE = (1/2)mv^2 ≈ (1/2) × 9.11 × 10^-31 kg × (6 × 10^5 m/s)^2 ≈ 1.64 × 10^-19 J ≈ 1.024 eV

φ = 3.1 eV - 1.024 eV ≈ 2.076 eV ≈ 2.1 eV