a) The energy levels for the valence electron of alkali atoms are found to be given approximately by the following formula: En,l=[n(l)]2RH, where (l) is the quantum defect, n is the principal quantum number, and l is the orbital quantum number of the electron. Explain why this formula applies, stating with reasons how you would expect (l) to vary with l. (b) The electronic configuration of the alkali metal francium is given by [Rn]7s. The first ionisation potential is equal to 4.07eV, and the average wavelength of the 8p7s transition is 428nm. (i) Find the values of (0) and (1) for francium. (ii) Estimate the average wavelength of the 7p7s transition. (iii) Find the minimum value of (2) that would allow the 8p6d transition to be observable in emission. (c) Explain how laser beams can be used to cool a gas of alkali atoms. d) In a laser cooling experiment on sodium (23Na), the laser is tuned to resonance with the D-line transition at 589nm, which has a radiative lifetime of 16ns. Estimate the maximum force that could be applied to each atom, and the deceleration that would result