PH515: Atomic and Molecular Physics
Problem Set - 2
Deadline to submit this tutorial is 08-09-2023
1. Estimate the lifetime of 2p state in hydrogen using Fermi-Golden rule.
2. Determine the effective nuclear charge Zeff in quadruple ionised carbon C4+ and corresponding binding energy using variational principle.
Compare your result of binding energy with available experimental result.
3. As discussed in class, calculate exchange (K1s2s ) energy of helium in
1s2s configuration.
4. (*) Consider two particles are represented by single particle orthonormal wavefunction ψa (x) and ψb (x). Calculate the expectation value of
the square of the separation distance between two particles h(x1 − x2 )2 i
when particles are distinguishable and in distinguishable, i.e., Bosons
and Fermions. Compare your results and comment on it.
5. (*) If the 3s electron in sodium did not penetrate the inner core then
its ionisation energy would be 1.51 eV by using hydrogen ionisation
formula. Because it does penetrate it sees a higher effective Z and its
energy is lower. Estimate the effective nuclear change of 3s electron in
sodium if the measured ionisation energy is 5.14 eV.
6. (*) Show that the polarisability (α) of Rydberg atom scale with seventh
power of principle quantum number qualitatively, i.e., α = n7 .
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