What we have been calling "s-block" "p-block" (main group elements), and "d-block" (transition elements) take on those names because they are filling orbitals with those designations!

Key point: when we create a new element from the previous one, we add one proton to the nucleus and one electron to the lowest energy orbital which has a "space" available.  This is the Aufbau Principle (Aufbau = "building up").

Key point #2: the electrons don't all keep piling into the lowest energy orbital (i.e. 1s)...  In fact there can only be two electrons per orbital.

Think about it: the d-block elements consist of a set of ten elements, but there are five d-orbitals in any particular subshell with a "d" designation.  These means there must be two electrons per orbital.  Similar arguments explain why the p-block is 6 elements wide, and the s-block is 2 elements wide.  The f-block (lanthanide and actinide elements) are not shown, but these are 14 elements wide as expected, since there are always 7 orbitals in a subshell with an "f" designation.

Pauli came up with a mathematical treatment which explains the behavior and this is summarized by his "Pauli Exclusion Principle."  He came up with a fourth quantum number, m_s.

m_s = spin quantum number
    * allowed values of +1/2 or -1/2.

Pauli Exclusion Principle: Only two electrons may "occupy" a given orbital in an atom, and these must have opposite "spin."  Stated another way: in any atom no two electrons can have the same 4 quantum numbers.

Quantum numbers can be used to describe electrons.  For hydrogen, there is only one electron, so the ground state configuration (electron in the lowest energy orbital) is 1s¹.  The quantum numbers which describe this electron are: n = 1, l = 0, m_l = 0, and m_s = +1/2.  The alternative with n = 1, l = 0, m_l = 0, and m_s = -1/2 is identical in energy unless the atom is placed in a magnetic field.

Hydrogen = 1s¹:

n = 1, l = 0, m_l = 0, and m_s = +1/2   or...
n = 1, l = 0, m_l = 0, and m_s = -1/2

For helium, there is still room for another electron in the 1s orbital so it's configuration is 1s².  One electron has m_s = +1/2, while the other must have m_s = -1/2.

Helium = 1s²:

electron 1: n = 1, l = 0, m_l = 0, and m_s = +1/2
electron 2: n = 1, l = 0, m_l = 0, and m_s = -1/2

For hydrogen atoms, there is only a single electron, and therefore no repulsion between electrons.  In this instance the only quantum number which determines the "energy" of an orbital is the principle quantum number n.

Orbitals which are identical in energy are termed degenerate.  For instance, in an H-atom, all 9 orbitals with n = 3 (3s, 3p, and 3d) are identical in energy = degenerate.

For all other atoms, electron-electron repulsions lift the degeneracy of the subshells for each value of n, and in many instances the principle quantum number is NOT the sole factor which governs the relative energy of a subshell.  To illustrate this point consider the drawings below again:
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Consider the following version:

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In this version of the table, the atomic numbers of the elements are listed as well as the subshell labels.  The periodic table then GIVES the electronic configuration if you know how to use it.

For instance: Sr (element #38) has a ground state electronic configuration of

Sr = 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s²

^{This is termed "spdf" notation.}

For all other atoms other than H, significant energetic differences arise between the various subshells for a given n.  It is always true that 4s < 4p < 4d < 4f, and 3s < 3p < 3d.  As it turns out, though, 4s is lower in energy than 3d (see the periodic table above) when the orbitals are being filled.  Is there another way of recognizing this peculiarity?

If one adds "n+l" and compares values for the various subshells, one can predict the order of filling reliably.  Higher values of "n+l" always correspond to higher energies.

4s vs. 3d
4s: n = 4,  l = 0, n+l = 4
3d: n = 3, l = 2, n+l = 5

Hence, 4s fills first because it has a lower value of n+l.

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What about "ties?"

4s vs. 3p
4s: n = 4,  l = 0, n+l = 4
3p: n = 3, l = 1, n+l = 4

We know that 3p fills first.  As it turns out when two subshells have the same value of n+l, the one with the lower value of n is the one which fills first.

The fact that elements within the same family (column) exhibit similar chemistry results from the fact that they have identical outer e- configurations.

If an electron spends more time near the nucleus, it is lower in potential energy than one which spends its time further from the nucleus.  The one which is further from the nucleus is said to be "shielded" by the interior (core) electron.

When one period of the periodic table is created by the Aufbau principle the electrons fill orbitals which are similar in energy (and hence distance from the nucleus).  Subsequent periods fill orbitals which, on average, are further from the nucleus.  Each set of electrons is termed a shell which is comprised of several subshells.

The interior electrons are termed "core electrons," while the electrons which fill the subshells in the period of interest are termed "valence electrons."  Each noble gas completes a period and hence has a closed shell electronic configuration.  The next electron goes into the next highest shell and is much further from the nucleus.

For instance, for Phosphorus, element #15:

P = 1s² 2s² 2p⁶ 3s² 3p³,

The electrons in the 1s, 2s and 2p subshells are "core" electrons, while the 3s and 3p electrons are "valence" electrons.  The 3s and 3p energy levels are much closer to each other but significantly higher than the 2s, 2p levels which, in turn, are much higher than the 1s level.  What about the shape of the the 3p vs 2p orbitals?  Both have similar "angular" dependence: being shaped like figure 8's.  However, the 3p level, being higher in energy, gives rise to a much more diffuse "radial" distribution: the electrons tend to spend more time further from the nucleus.  This is tantamount to saying that "the 3p orbital is BIGGER than the 2p orbital."

The valence electrons are most important (as are the valence orbitals) for a number of reasons.  Valence electrons are the "outermost" electrons.  These are shielded by the core electrons from being attracted to the nucleus and hence are highest in energy.  In the formation of cations, it is the valence electrons that are removed.  Similarly, when an element accepts an electron to form an anion, it is the lowest empty orbital which becomes occupied.  In the formation of covalent bonds (between two non-metals) the electrons which participate the most in mutual sharing are those which are furthest from the nucleus, since these are most easily attracted by the other nucleus (and vice versa).

Closed shells may be abbreviated by the symbol for the noble gas with the same number of electrons in square brackets.  Our previous example, Sr, has an electronic configuration which may be abbreviated as:

Sr = [Kr] 5s².

Similarly, the halogens tend to form -1 anions in order to attain the closed shell electronic configuration of the next noble gas.  The chalcogens in Gp16 form -2 anions and the alkaline earth metals of Gp2 form +2 cations (if they are involved in ionic compounds) for the same reasons.  Rule 7 for oxidation state assignments is based on this principle.  (see section 3.4 notes)

One final point concerns the filling of subshells themselves.  We use "orbital diagrams" where boxes represent orbitals, and up/down arrows represent electrons with opposite spins.

Consider nitrogen (N = element # 7).

It's electronic configuration is 1s²2s²2p³ as based on it's position in the periodic table.  Two electrons populate both the 1s and 2s orbitals, and these must have opposite spin.  How do the 3 electrons populate the 2p subshell?  Based on electrostatic principles it makes perfect sense that these would "choose" to enter different orbitals since this maximizes their spatial separation (and hence minimizes their repulsion).  What about the "spins?"  It turns out that the lowest energy configuration is the one in which all of the spins are aligned.  This observation is termed Hund's rule: electrons fill a subshell in such a way as to maximize the number of unpaired electrons with the same spin.  Below are a few orbital diagrams which illustrate Hund's rule.

All atoms and molecules that have all of their electrons paired up are termed "diamagnetic."  One interesting property of diamagnetic substances is that they repel magnetic fields.  In contrast, atoms or molecules that exhibit unpaired electrons in their ground states are termed "paramagnetic."  Paramagnetic substances are attracted to magnetic fields.

Which of the 2nd period atoms (Li, Be, B, C, N, O, F, Ne) is(are) paramagnetic?  Answer: Li, B, C, N, O, F.

Which atom of the second period exhibits the most unpaired electrons in it's ground state?  Answer: N (3).

When an electron enters the same orbital as another we say that it "pairs up."  Because electrons in close proximity repel one another there is an energetic cost associated with such a process termed the pairing energy.  Occasionally subshells in a particular atom are so close in energy that the pairing energy is larger than the difference in the energy of the subshells.  It becomes energetically favorable to place the electron in a higher energy orbital rather than pairing it with another electron in a lower energy one.

This situation arises a few times in the periodic table, most notably when the electron added to a higher level becomes part of a half-filled shell.  Half-filled shells maximize the spatial separation of electrons and also give rise to a spherical electron density distribution.  Hence this situation is energetically favorable.

Examples: spdf notation

Cr = [Ar] 4s¹ 3d⁵
Mo = [Kr] 5s¹ 4d⁵
Gd = [Xe] 6s² 5d¹ 4f⁷

By the time we finish filling the d-subshells the principle quantum number starts to play a dominant role in determining the energy of the subshell.  This gives rise to another "exception" exhibited by the coinage metals Cu-Ag-Au.  All of these have a valence electron configuration of ns¹ (n-1)d¹⁰.