A light wave described by the electric field E = E₀ [ (2 10¹⁵ t) + (4 10¹⁵ t)] (in SI units) falls on a metal surface having a work function of 3.28 eV. The emitted photoelectrons are directed into a uniform transverse magnetic field of 7.5 10⁻⁵ T. The maximum radius of the circular path traced by the photoelectrons is: (Given: Planck's constant h = 4.14 10⁻¹⁵ eV s, mass of electron m = 9 10⁻³¹ kg, charge of electron

Step-by-step solution

The electric field contains two angular frequencies: ₁ = 2 10¹⁵ rad/s ₁ = 1 10¹⁵ Hz ₂ = 4 10¹⁵ rad/s ₂ = 2 10¹⁵ Hz The maximum kinetic energy is produced by the highest frequency component, ₂ = 2 10¹⁵ Hz. The energy of the corresponding photon is: E = h ₂ = (4.14 10⁻¹⁵ eV s ) (2 10¹⁵ Hz ) = 8.28 eV. Using Einstein's photoelectric equation, the maximum kinetic energy is: K_ max = E - = 8.28 eV - 3.28 eV = 5.0 eV. Converting this kinetic energy into Joules: K_ max = 5.0 1.6 10⁻¹⁹ J = 8.0 10⁻¹⁹ J. The maximum momentum