Question

(i) Given that angular momentum of an electron in a hydrogen atom is = ??? , where m is the electron mass, v is its velocity and r is the radius of orbit, use the de Broglie relation to derive a relation to prove the angular momentum of the electron is quantized. Note: You may assume integer multiples of half-wavelengths are required. [8 marks]

(ii) Using the relation derived in part (i), derive an expression for the energy of an electron in any energy level n, and draw a typical energy band diagram resulting from this equation. Note: The centripetal force is ? = ?? 2 ? ⁄ The Coulomb force ? = ?? 2 4???? ⁄ 2 You may assume integer multiples of half-wavelengths are required.

(iii) The work function for lithium is 300 kJ/mole. What is the wavelength of light that will remove an electron from an atom in lithium metal so that it has an ejected energy of 0.5 eV once free of the lithium atom? Note: 1 kJ/mol = 0.01036410 eV; me = 9.10938 × 10-31 kg

Answer 1