Slides9

Lecture #7, September 13, 2006

These "slides" represent highlights from lecture and are neither complete nor meant to replace lecture. It is advised not to use these as a reliable means to replace missed lecture material. Do so at risk to healthy academic performance in 09-105.

Lecture Outline

Many-electron atoms

Hund's rules for most stable configurations

Configuration sequences

The Periodic Table

Effective nuclear charge and electron configurations

Valence electrons

Chemical "groups"

Many-electron systems

Pauli Exclusion principle

Effective nuclear charge

Photoelectron spectra of atoms

Electron configuration

Recalling that the photoelectric effect can be exploited to obtain "binding energies" of an electron to some anchor (metal surface, gaseous molecule or atom), we can look at binding energies of an electron.

When we go from H to He, despite the fact that the nuclear charge has doubled and that Bohr's energy formula suggests the binding energy might then have quadrupled, it increases by only 80%. You should be able to show that the effective nuclear charge holding a 1s electron in He is about 1.3.

For element number 3, we note two photoelectron peaks, one from each of the orbitals containing electrons. Depending on which single electron is ejected by the photon, the electron has one of two possible final kinetic energies.

Boron is element 5. There are 5 electrons distributed as: two in the inner core, 1s orbital; 2 in the valence 2s orbital; and 1 in the valence 2p orbital. The latter is easiest to remove and, when kicked out by the photon, shows up with the greatest kinetic energy therefore.

The enery levels of the one electron in the hydrogen atom.

The energy levels of the various s-states in a one-electron system. The energy needed to remove an electron from hydrogen in its "ground state" is shown. This can be determined through photoelectron spectroscopy (an application of the photoelectric effect), for example.

From the values of the electrons's energies, you can also get the photon energies (and wavelengths) involved in transitions between initial and final electron states.

Consider lithium's ground state (Z=3). The "inner core" of electrons comrpises the filled 1s shell. The "outer electrons" are the valence electrons. In this case, the 2s electron is the valence electron for lithium.

We can indicate how electrons are placed in orbitals by configuration diagrams. The one shown here corresponds to the ground state for lithium (Z=3).

Because the effective nuclear charge is determined by how much the nucleus is screened by other electrons, the 2p orbitals are not as tightly bound as the 2s orbital. This is the ground state for 5-electron systems.

The arrangement of orbitals in increasing energy can be shown horizontally too, as in the text. For the sixth electron, there are several locations to chose from. This is the lowest energy choice, the most stable.

This arrangement is another possible choice for 6 electrons, but is an excited state for a 6-electron system.

Here are seven and eight electron systems (in addition to six) corresponding to ground state arrangements of electrons in nitrogen and oxygen. On the last line is written another form of the electron configuration for atomic oxygen in its ground state.

Other electron configuration examples: fluorine and sodium.

Excited states for the valence electron in lithium

The idea that an effective nuclear charge can embody all the various "penetration" and "screening" effects due to the many electrons around an atomic nucleus. Penetration refers to an electron having some of its density inside the region where inner core electrons are most likely to be found. Screening refers to the reduction of positive charge felt by an outer electron due to the presence of inner, negatively charged electrons.

The ionization energy of the highly excited valence electron, starting in the 5s state of lithium, corresponds very closely to the ionization energy of a hydrogen atom which has Z = 1. This is because the lithium 5s electron is far away from the nucleus with charge +3 and the inner core of electrons which contribute a charge of -2 and through which the far-away electron penetrates only very slightly.

That excited valence electron, if in a p-orbital, penetrates the inner core even less than if an s-orbital. The effective nuclear charge is much closer to unity. The effectiveness of penetration decreases as the electron in question moves to higher and higher orbitals. The transition shown corresponds to 2p --> 2s and involves red light.

Continuing our discussion of effective nuclear charge, we move on to the sodium atom with Z=11. The electron configuration is 1s²2s²2p⁶3s¹ or [₁₀Ne]3s¹. The valence electron is the 3s electron, which can be promoted to the excited states illustrated. Note that because of the great penetrating probability of an electron in the s-orbital, the 4s becomes lower in energy than the 3d orbital. The yellow (590 nm) emission line of an excited Na is indicated.