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

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.

Iodine molecule dissociates into atoms after absorbing light of 4500 Å. If one quantum of radiation is absorbed by each molecule, calculate the kinetic energy of iodine atoms. (Bond energy of I₂ = 240 kJ mol^-1)

Estimate the difference in energy between 1st and 2nd Bohr orbit for a hydrogen atom. At what minimum atomic number, a transition from n = 2 to n = 1 energy level would result in the emission of X-rays with $$\lambda = 3.0 \times {10^{ - 8}}$$? Which hydrogen atom like species does this atomic number correspond to?