A consideration of how much an outer electron feels the effect of a nuclear charge after shielding effects of other electrons. quantum mechanical correction for exchange energy consideration due to exact electron configurations is then explored.
The electron configuration of an atom dictated by quantum mechanics has a profound impact on the attraction that an electron feels towards the positively charged nucleus that it surrounds. Inter-electron repulsion effects in multi-electron systems mean that the first ionisation energy of an atom can vary in non-obvious ways across a Period in the Periodic Table. Quantifying this effect as an effective nuclear charge helps to simplify our thinking about how much different types of electron environment shield (or screen) this positive charge. Using Slater's rules is a quick method for gaining insight into these effects by quantifying the shielding (screening) as a constant that can be calculated. Hence, a multi-electron system (a 3-body problem, or many-body problem) can be approximated crudely to a hydrogen-like atom (a 2-body problem). The physics and chemistry of such a system is much more easy to model, partly due to Schrodinger equation setups based on these systems are more tractable, and sometimes analytically solvable too. This leads to the idea of using standing wave solutions to the Schrodinger equation as atomic orbitals, which then extend the ideas of bonding commonplace to many areas of chemistry.
The video introduces the idea of quantum mechanical exchange energy, a stabilising effect for certain electron configurations. When electrons are in degenerate orbitals of the same type, the prefer to be spin parallel in order to maximise this exchange energy. Quantum mechanical exchange energy arises because electrons are fermions, and due to the Pauli principle, their wavefunctions must be antisymmetric with respect to changes in labels in spin states. This means that is the electron spins are parallel, a Fermi hole is generated and this quantum mechanical event prevents the electrons getting within a certain distance of each other at all times. Hence, any coulombic repulsive forces are reduced as they depend strongly on charge separation. Certain electron configurations of atoms have multiple pairs of parallel spins, and hence many Fermi holes, and so on first ionisation will lose a lot of exchange energy in the process. Consequently these atoms are a bit harder to ionise than we might expect by considering the effective nuclear charge alone. These effects are particularly noticeable for the atoms that have a complete half-shell or full-shell configuration. The absolute "stability" of the half-shell and full-shell configurations (or noble gas configuration) is sometimes misattributed to these atoms. In reality, it is the specific process of ionising that it anomalously requiring more energy than expected (as in final state take away the initial state). Stability is not an absolute property, only relative, and so should only be used relative to something else.
The energy levels of a hydrogen-like atom are given by combining the nuclear charge with the principal quantum number n. The proportionality is given by the Rydberg constant, which can be quoted in whatever units you want to deal with atomic orbital energies in; often this is electron-volts (eV), or you send all of these equations into atomic units (where energy is measured in Hartrees).
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