Explain what each quantum number in a quantum number set tells you about the electron. Compare and contrast the locations and properties of two electrons within an atom that have the quantum number sets (3, 2, -1, +½) and (3, 1, -1, +½).
n = energy, or equivalently typical distance from the nucleus l = angular momentum m_l = orientation of angular momentum axis with respect to some external axis, e.g. an applied magnetic field. m_s = orientation of spin axis with respect to some external axis, also e.g. an applied magnetic field. Note that in the absence of an external axis, e.g. an external magnetic field, m_l and m_s are fairly meaningless, meaning electrons can easily be in superpositions of states with different m_l and/or m_s. In terms of your two states: the first is... * at about the same distance from the nucleus, and has a roughly similar energy and exactly the same if both electrons are in an H atom. * has a larger angular momentum, and hence, if both electrons are in multi-electron atoms, a slightly higher energy. If the there is no external field, the other two quantum numbers are nearly meaningless. But if we assume there is such a field, then... * the first has its axis of angular momentum slightly antiparallel to the external axis. (If m_l = -2 it would be exactly antiparallel), and the spin axis is parallel. * the second has its axis of angular momentum antiparallel to the external axis, and its spin axis parallel.
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