For example:
Select the correct set of quantum numbers (n, l, ml, ms) for the highest energy electron in the ground state of oxygen.
Select the correct set of quantum numbers (n, l, ml, ms) for the first electron removed in the formation of a cation for gallium, Ga.
I understand the quantum rules, (n must be a positive whole #, l can be any positive number one less than n, and ml can be -l to +l, and ms can be -1/2 or +1/2) I can identify allowed combinations, but we didn't go over how to assign quantum numbers to specific electrons. Can someone explain?
Select the correct set of quantum numbers (n, l, ml, ms) for the highest energy electron in the ground state of oxygen.
Select the correct set of quantum numbers (n, l, ml, ms) for the first electron removed in the formation of a cation for gallium, Ga.
I understand the quantum rules, (n must be a positive whole #, l can be any positive number one less than n, and ml can be -l to +l, and ms can be -1/2 or +1/2) I can identify allowed combinations, but we didn't go over how to assign quantum numbers to specific electrons. Can someone explain?
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The position of each element in the periodic table not only corresponds to a number of electrons or protons, but also to a certain ground-state electron configuration; you can determine those following Pauli's Aufbau principle, which states that electrons in the ground state occupy orbitals in such a way that results in the lowest overall energy; Hund's rule is kind of an appendix to this that states that in the case of degenerate orbitals, the unoccupied ones will be occupied first (with electrons of identical ms), and only after no more empty ones are available do we introduce paired electrons. The energy ordering of the orbitals is not quite trivial but generally the arrows in this picture:
http://upload.wikimedia.org/wikipedia/co…
Let us consider your example: Oxygen has 8 electrons; the ordering of orbitals is 1s, 2s, 2p, 3s, 3p, 3d, etc.; we fill the maximum 2 electrons into the 1s orbital, the same number into the 2s orbital and the remaining four occupy the three degenerate 2p orbitals, leaving us with an electron configuration (1s)2(2s)2(2p)4 (numbers outside parantheses usually written as superscripts); according to Hund's rule, one electron goes into each of the three sublevels (ml = -1, 0, 1) and we're left with one electron to deal with; it will occupy one of the three sublevels under spin-pairing (i.e. its ms is the opposite sign of the one already present). As, in the approximation most people usually work with, the three 2p sublevels are degenerate, the question is kind of strange; the electron can go into any of the three orbitals, as they are degenerate and the spin quantum number is indeterminate, anyways, unless we apply an external field and disturb the system; however, n is certainly 2 and l is certainly 1 for that electron.
One more hint: For large atoms, you can neglect the previous noble gas configuration, which saves you a lot of writing; just count the electrons you have to add from the beginning of the period to your element and fill them in starting with the (ns) orbital, n being the number of your period.
http://upload.wikimedia.org/wikipedia/co…
Let us consider your example: Oxygen has 8 electrons; the ordering of orbitals is 1s, 2s, 2p, 3s, 3p, 3d, etc.; we fill the maximum 2 electrons into the 1s orbital, the same number into the 2s orbital and the remaining four occupy the three degenerate 2p orbitals, leaving us with an electron configuration (1s)2(2s)2(2p)4 (numbers outside parantheses usually written as superscripts); according to Hund's rule, one electron goes into each of the three sublevels (ml = -1, 0, 1) and we're left with one electron to deal with; it will occupy one of the three sublevels under spin-pairing (i.e. its ms is the opposite sign of the one already present). As, in the approximation most people usually work with, the three 2p sublevels are degenerate, the question is kind of strange; the electron can go into any of the three orbitals, as they are degenerate and the spin quantum number is indeterminate, anyways, unless we apply an external field and disturb the system; however, n is certainly 2 and l is certainly 1 for that electron.
One more hint: For large atoms, you can neglect the previous noble gas configuration, which saves you a lot of writing; just count the electrons you have to add from the beginning of the period to your element and fill them in starting with the (ns) orbital, n being the number of your period.