Filling Electron orbitals
We can now see what electron configurations are possible for the lowest-energy, resting or ground-state of an atom.
As we have said, each orbital can accommodate 0, 1 or 2 electrons, but no more: if two are accommodated, then they will have different values of ms - the spin quantum number of +0.5 and -0.5. Pauli's Exclusion Principle states that "in any one atom, no two electrons may have all four Quantum Numbers the same".
For hydrogen 1 s 1 (either m subscript s value permitted) should be self-evident. You will also be happy with 1s 2 for helium (one electron with each value for ms), although it should be mentioned that the reason why this is preferred over 1s 1 2s 1 is because the energy separation between 1s and 2s is very large as compared with the energy required to pair two electrons in the same orbital. You should remember that energy is required to overcome the mutual repulsion of two electrons confined into the same volume of space (or orbital); on other occasions the comparison will be more critical, indeed our life depends on it!
At lithium we have 1s22s1 or [He]2s1, and at beryllium 1s22s2 or [He]2s2. We should note that the energy separation between 2s and 2p is still greater than the pairing energy, so a configuration of [He]2s12p1 is higher in energy than the ground-state, but requires not too much additional energy, and is the 'excited-state' which we shall see leads to the ability of beryllium to form two covalent bonds in so-called sp hybridisation. Notice that there is now an energy difference between 2s and 2p orbitals. There is no such difference for atomic hydrogen, where all orbitals of the same principal quantum number have the same energy; which is why the lines in the Lyman, Balmer and Paschen series do not split for hydrogen, but do so for other elements. However, in all elements where these orbitals are the occupied 'valence' orbitals, this energy difference will always be present.
The explanation for this phenomenon is in the 'screening' effect on the electron from the full attractive influence of the positive charge on the nucleus, by other electrons in the electron configuration (never a problem for hydrogen because it has no other electrons to shield it). Each electron feels an attraction to the nucleus (e- attracted to Z+ at a point) which is diminished by the net repulsion of other electrons. The radial and angular distributions in space of these electrons means that they may not fully cancel out the attractive force of the nucleus on the electron in question. As a bulk unit the electrons do electrically neutralise the protons in the nucleus. For instance, if you draw out a px and a py orbital, you should see that an electron in one is unlikely to perfectly shield an electron in the other from the nuclear attraction of "its" proton since the p-orbitals are directional along different axes: this looks particularly convincing if the orbitals are drawn as very directional.
The net effect of nuclear attraction and electron repulsion leads to an idea of differential rules for shielding by electrons in certain types of orbitals for electrons in other types of orbitals and you will find quantitative values in the literature. The end result is an "effective nuclear charge" felt by each electron, given the symbol Zeff (or sometimes Z*) which is always equal to, or greater than, unity. For the particular case of 2s and 2p orbitals, although both orbitals have zero values of the radial distribution function (RDF) at the nucleus (necessarily so), the 2s has a radial nodal surface which gives an electron in it a small, but finite, chance of 'being' near to the nucleus and penetrating the space occupied by the 1s electrons: a 2p electron does not have this advantage, so the 2s orbital is a preferred location for the first n = 2 electron and lies lower in potential energy than the 2p orbital. Thus it is occupied first at Li and filled at Be before the first 2p electron enters at boron, which has electron configuration [He]2s 22p1.
So what happens at carbon which is [He]2s22p2 ? Three distinct possibilities seem to exist.
Hunds' Rule will tend to favour electron configurations with unpaired electrons. Such electron configurations make for "paramagnetism" in the free atoms; that is they would be attracted towards the strong region of an applied magnetic field (the lines of force are concentrated within the paramagnetic substance). The explanation of this "inherent" magnetism is that, in classical terms, a spinning, charged particle will generate a magnetic field. Compare this with pairs of electrons with opposite spin (quantum numbers) that will create equal and opposed magnetic fields which will cancel out each others effect leading to "diamagnetism ". A diamagnetic substance has no inherent magnetism, and only acquires magnetism when placed in an applied magnetic field, when the induced magnetism opposes that of the applied field: thus diamagnetic substances are repelled from the applied magnetic field (lines of force are less concentrated within a diamagnetic sample than outside it).This building up, or aufbau, of electron configurations continues from Ne to Ar in exactly the same way as from He to Ne, and with the same explanations.
But at potassium a very important and unexpected thing happens. You might have expected potassium to have an electron configuration [Ar]3d1 since d orbitals are now available for the first time: but it does not. The actual electron configuration is [Ar]4s1. The same principle is operating which filled 2s level before the 2p at Li (and Be), and filled 3s before 3p at Na (and Mg). The 4s orbital has three radial nodal surfaces, whereas a 3d orbital has none. Thus the 4s orbital penetrates the [Ar] core better and is filled first. The penetration could have been predicted, but the filling of an orbital from a higher principal quantum shell before one from a lower shell (4s before 3d) could not! Philosophically, one might enquire whether this particular law of quantum physics is just plain "good luck", since its consequences are so important to the versatility of chemistry and to our existence in the biochemical form that we have; others of a more religious bent may wish to invoke a higher purpose.
The changes in the relative energies of the various quantum shells and sub-shells are illustrated below, where you see that 4s dips below 3d just at the point where one or other is about to be filled.
RELATIVE ENERGIES OF ORBITALS DIAGRAMME HERE
Given their energetic proximity, the preference of 4s over 3d is as explained, but their proximity does not seem to have been inevitable. But it happened, and as a consequence of differential shielding the 3d and 4s remain energetically close throughout the subsequent filling of the 3d shell after the 4s has filled at calcium. Indeed at chromium [Ar]4s13d5 and copper [Ar]4s13d10, the half-filled and filled 3d shells are achieved 'one element early' at the expense of the transfer of a 4s electron to 3d - vindicating Hund's Rule of Maximum Multiplicity. Many of these "transition metals" are vital to life, and you will hear much more about them in other courses.
This organisation of elements according to electron configuration led eventually to the 'Periodic Table' as we know it today, most aspects of the Periodic Table will not be discussed here. A couple of properties will be discussed now because they can be explained in terms of some of the concepts that have already been introduced.
The first thing to note is that the definition is not totally clear, since the electron distribution is one of diminishing (but never actually zero) probability with increase of distance from the nucleus. The definition of radius which is used is "half the closest approach found in the solid element", or "half of the covalent bond length".
We would expect radius to increase on descending a Group, for example Group 1 - lithium to caesium, and it does (see Table below): the explanation is simply that for each member of a Group, an additional shell of electrons (or set of sub-shells) is added with a similar external configuration carrying the valence electrons (ns1 for Group 1). However, on crossing a period (for example, lithium to fluorine), we are adding electrons to the same principal quantum shell (n = 2 for Li to F), and the shielding of, for example, an electron in one p-orbital for an electron in another p-orbital is less than perfect; so Zeff increases as we move across a period, and the radius decreases (see Table below).
| Element | Radius (pm) | First ionisation energy (kJ mol-1)
|
|---|---|---|
| Li | 123 | 520
|
| Na | 156 | 495
|
| K | 203 | 418
|
| Rb | 216 | 403
|
| Cs | 235 | 374
|
| Li | 123 | 520
|
| Be | 89 | 900
|
| B | 82 | 800
|
| C | 77 | 1086
|
| N | 70 | 1403
|
| O | 66 | 1314
|
| F | 64 | 1681
|
TWO GRAPHS HERE of Data above
The radii quoted are covalent radii; the elemental radii for Group 1 metals are approximately 32pm greater.
Ionisation energy is the energy required to raise the outer most electron to the n = infinity i.e. move the electron to an infinite distance away from the nucleus (remember the hydrogen atom Lyman series). On descending Group 1, this first ionisation energy decreases progressively as the more distant electron becomes more easy to remove against the diminishing coulombic forces and Zeff remains constant at approximately unity throughout (see Table above). You might therefore expect ionisation energy to increase as we cross from Li to F and indeed it does so, but not regularly (see Table above). For further information on ionisation energy trends and other related material, I have provided a link to the CHEMDEX ionisation site.
The interruptions in the rise between Be and B, and between N and O are explained as follows. At boron, the electron removed is from a 2p orbital which is better shielded from the nucleus than is a 2s electron, since the former has zero radial nodal surfaces, whereas the latter has one radial nodal surface and thus a small but significant probability of lying near to the nucleus. At oxygen, the electron removed is one of a 2p2 pair (for the three previous elements, the ionised electron had been unpaired) and is therefore more easily ionised since the other electron in its orbital 'repels' it.