The radiation emitted, when an electron jumps from n = 3 to n = 2 orbit is a hydrogen atom, falls on a metal to produce photoelectron. The electrons from the metal surface with maximum kinetic energy

Question

The radiation emitted, when an electron jumps from n = 3 to n = 2 orbit is a hydrogen atom, falls on a metal to produce photoelectron. The electrons from the metal surface with maximum kinetic energy are made to move perpendicular to a magnetic field of 1 320 T in a radius of 1 0 - 3 m . Find the work function of metal.

TestHub · Accepted Answer

1.03 eV E 3 - E 2 = 13.6 1 2 2 - 1 3 2 = 13.6 × 5 36 = 1.89 eV Photoelectrons with k E m a x are moving on circular path. r = m v q B ⇒ m v = q B r ⇒ P = q B r ⇒ P = 1.6 × 1 0 - 19 × 1 3200 × 1 0 - 3 ⇒ 1 2 × 1 0 - 24 = 5 × 1 0 - 25 kg ⁡ m / s Energy of photoelectron ⇒ K E m a x = P 2 2 m ⇒ K E m a x = 25 × 10 - 50 2 × 9.1 × 1 0 - 31 × 1.6 × 1 0 - 19 e V ⇒ K E m a x = 0.86 e V Now use Einstein equation h v = ϕ + K E m a x ⇒ 1.89 = 0.56 + ϕ ; ⇒ ϕ = 1.03 eV

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