The work function of a metal is 1 eV. Light of wavelength 3000 Å is incident on this metal surface. The velocity of the emitted photo-electrons will be:

Explanation

Convert the wavelength to meters: 3000 Å = 3000 x 10-10 m = 3 x 10-7 m Calculate the energy of the incident photon (E) using the formula E = hc/λ, where h is Planck's constant (6.626 x 10-34 Js) and c is the speed of light (3 x 108 m/s). E = (6.626 x 10-34 Js * 3 x 108 m/s) / (3 x 10-7 m) = 6.626 x 10-19 J Convert the work function (Φ) from eV to Joules: 1 eV = 1.602 x 10-19 JCalculate the kinetic energy (KE) of the emitted electron using KE = E - Φ. KE = (6.626 x 10-19 J) - (1.602 x 10-19 J) = 5.024 x 10-19 JCalculate the velocity (v) of the electron using KE = 1/2 mv2, where m is the mass of an electron (9.109 x 10-31 kg). v = √(2KE/m) = √((2 * 5.024 x 10-19 J) / (9.109 x 10-31 kg)) ≈ 1.05 x 106m/s