Consider the hydrogen atom to be a proton embedded in a cavity of radius a₀ (Bohr radius) whose charge is neutralised by the addition of an electron to the cavity in vacuum, infinitely slowly. Estimate the average total energy of an electron in it's ground state in a hydrogen atom as the work done in the above neutralisation process. Also, if the magnitude of the average kinetic energy is half the magnitude of the average potential energy, find the average potential energy.

A 3.00 g sample containing Fe₃O₄, Fe₂O₃ and an inert impure substance is treated with excess of KI solution in presence of dilute H₂SO₄. The entire iron is converted into Fe²⁺ along with the liberation of iodine. The resulting solution is diluted to 100 ml, A 20 ml of the diluted solution requires 11.0 ml of 0.5 M Na₂S₂O₃ solution to reduce the iodine present. A 50 ml of the diluted solution, after complete extraction of the iodine requires 12.80 ml of 0.25 M KMnO₄ solution in the dilute H₂SO₄ medium for the oxidation of Fe²⁺. Calculate the percentages of Fe₂O₃ and Fe₃O₄ in the original sample.

The orbital angular momentum of an electron in 2s orbital is

Calculate the wave number for the shortest wavelength transition in the Balmer series of atomic hydrogen.