A metal surface is illuminated by a radiation of wavelength 4500 A ∘ . The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90 ° with the magnetic field. If it starts revolving in a circular path of radius 2 mm , the work function of the metal is approximately

Step-by-step solution

From the Einstein's photoelectric equation K = h c λ - ϕ ⇒ ϕ = h c λ - K Now R = m v B q ⇒ v = R B q m ⇒ K = R 2 B 2 q 2 2 m Therefore, ϕ = h c λ - R 2 B 2 q 2 2 m = 6 . 63 × 10 - 34 × 3 × 10 8 4500 × 10 - 10 - 2 × 10 - 3 × 2 × 10 - 3 × 1 . 6 × 10 - 19 2 2 × 9 . 1 × 10 - 31 ⇒ ϕ = 4 . 42 - 2 . 25 × 10 - 19   J = 2 . 27 1 . 6   eV = 1 . 36   eV