Electronic Structure

The electronic structure (electronic configuration) of an atom refers to the arrangement of electrons around its nucleus.

There is something useful to remember; the maximum number of electrons that can be contained within a Principal Quantum Level, n, is given by 2n² (2 x n²).

Immediately, this may conflict with your understanding of the concept at GCSE; in the energy level n = 3, there is a maximum of 18 electrons. At GCSE only the first 20 elements are considered. The electronic structure of calcium is 2.8.8.2.

This is what happens. Eight electrons enter into the n = 3 level, followed by two more being placed in the n = 4 level. The n = 3 level now accommodates another ten electrons to make a maximum total of 18. But when it comes to losing electrons in ion formation (e.g. Ca²⁺), the two electrons in the n = 4 level are removed first. The element Zinc has the electronic structure 2.8.18.2 but, take care, it is not in Group II of the Periodic Table. Following on from Zn, the n = 4 level continues to fill with electrons.

Some Evidence for the existence of Principal Quantum Levels

A plot of the log₁₀ of the successive ionisation enthalpies for an element (e.g. K) against the no. of ionisation provides evidence for the existence of Principal Quantum Levels and the number of electrons that can be contained in each.

Some Evidence for the existence of sub-divisions with Principal Quantum Levels

The Quantum Theory page refers to the Principal Quantum Number, n, arising from a solution of the Schrödinger equation, and the quantised nature of electrons in atoms. The Spectra and Electrons page describes the origin of atomic emission spectra. At first examination, the spectral line in the hydrogen atomic emission spectrum, arising from the electron transition from n = 2 to n = 1, for example, appears to be a single line. But at a very high resolution it is found that two lines exist at very close frequency (or energy).

This suggests there are sub-divisions (or sub-levels) within Principal Quantum Levels. Something to note is that the number of sub-levels within a Principal Quantum Level is the same as the Principal Quantum Number, n. The n = 2 level has two sub-levels, offering an explanation for the two spectral lines observed above.

A plot of the first Ionisation Enthalpies of the successive elements (e.g. H to Zn) also provides some evidence for sub-divisions within Principal Quantum Levels.

The above plot shows the underlying increase in first ionisation enthalpy in going from left to right across a Period of the Periodic Table. Evidence of sub-divisions with Principal Quantum Levels is suggested by the small 'unexpected' decrease in first I.E. in going from, for example, Be to B, and also from N to O. This plot also illustrates periodicity amongst the elements.

Solution of the Schrödinger equation - Atomic Orbitals

Although the Schrödinger equation is difficult to solve except in simple cases, its results can be described. Both the exact position and exact energy of electrons in atoms cannot be known at the same time. The electron can therefore move anywhere relative to the nucleus without changing its energy. A solution of the Schrödinger equation does, however, describe the probability of finding the electron in a volume of space around the nucleus. For the hydrogen atom in its ground state, the space in which the electron is likely to be found can be 'pictured' as a spherical cloud of negative charge, called its atomic orbital.

Remember, the number of sub-levels equals n. Thus, n = 1 has one sub-level (or subshell). n = 2 has two sub-levels, and so on.

The sub-levels (or atomic orbitals) are represented by the letters s, p, d, f. All the orbitals in the same sub-level have the same energy. They increase in energy as they become more distant from the nucleus.

These atomic orbitals have different sizes, shapes, and spatial orientations. Only s orbitals are spherical, and they occur singly. p orbitals are often described as dumb-bell shaped, occurring in groups of three orientated along the x-, y- and z-axes. d orbitals exist in groups of five, becoming more complex in their shapes and orientations. f orbitals occur in groups of seven. Placed on a set of x-, y- and z- axes, the nucleus of the atom is at the origin. But remember, the shapes of these atomic orbitals do not represent reality; they are pictorial representations of the mathematical solutions of the Schrödinger equation.

Each atomic orbital can hold a maximum of two electrons. [Wolfgang Pauli discovered this from a study of atomic specra and the periodic table - you will need to look up the Pauli exclusion principle.] Therefore, a set of three p orbitals can hold a maximum of six electrons, a set of d orbitals a maximum of 10 electrons, and a set of f orbitals a maximum of fourteen electrons.

Some of the above points are summarised below:

Arrangement of Electrons in Atoms

The hydrogen atom has only one electron, but the presence of several electrons creates complex mathematical problems because electrons repel each other. Fortunately, the similarities between many-electron atoms and the hydrogen atom are sufficiently similar that we may use orbitals like those found in the H atom to describe their electron configurations.

The diagram below shows the order of increasing energy of atomic orbitals.

The energy levels become tangled as the atomic number increases. For example, up to atomic number 18 the 3d orbital is below the 4s. But at atomic number 19, the 4s dips below the 3d. The diagonal rule, also shown above, is useful in predicting electron configurations of atoms. Though the diagonal rule does not flow smoothly from theoretical calculations, it does account for the order of elements in the periodic table.

In distributing the electrons in the ground states of atoms, each added electron will enter the orbitals in the order of increasing energy. For the first four elements - ₁H, ₂He, ₃Li, ₄Be - electrons are placed in the 1s atomic orbital (for H and He) and then into the 2s orbital (for Li and Be). Since all three orientations of the p orbitals is equivalent, which p orbital (p_x, p_y or p_z) is then used is not important in ₅B. But for carbon, do the two p electrons occupy one or two orbitals? The Hund rule answers this question. It says that: electrons stay unpaired in orbitals of the same energy until each such orbital has at least one electron in it. The Hund rule is most likely associated with repulsion effects between electrons. Where two electrons occupy an atomic orbital, they are in opposite spin.

The diagram below allows the electron configurations of some elements to be explored. Move the mouse pointer over the element name. Look carefully at the electron configurations of the transition elements Cr and Cu. Note the experimental values shown do not agree with the predicted ones.

Hydrogen	H	1s
Helium	He	1s2
Lithium	Li	1s2 2s1
Beryllium	Be	1s2 2s2
Boron	B	1s2 2s2 2p1
Carbon	C	1s2 2s2 2p2
Nitrogen	N	1s2 2s2 2p3
Oxygen	O	1s2 2s2 2p4
Neon	Ne	1s2 2s2 2p6
Sodium	Na	1s2 2s2 2p6 3s1
Sulphur	S	1s2 2s2 2p6 3s2 3p4
Argon	Ar	1s2 2s2 2p6 3s2 3p6
Potassium	K	1s2 2s2 2p6 3s2 3p6 4s1
Calcium	Ca	1s2 2s2 2p6 3s2 3p6 4s2
Scandium	Sc	1s2 2s2 2p6 3s2 3p6 3d1 4s2
Vanadium	V	1s2 2s2 2p6 3s2 3p6 3d3 4s2
Chromium	Cr	1s2 2s2 2p6 3s2 3p6 3d5 4s1
Manganese	Mn	1s2 2s2 2p6 3s2 3p6 3d5 4s2
Iron	Fe	1s2 2s2 2p6 3s2 3p6 3d6 4s2
Copper	Cu	1s2 2s2 2p63s2 3p6 3d10 4s1
Zinc	Zn	1s2 2s2 2p6 3s2 3p6 3d10 4s2

The arrangement of electrons in atoms can be investigated further and related to their positions in the periodic table via the Aufbau Principle page.

A shorthand method of writing electron configuration is illustrated below:

₁₂Mg   [Ne]3s²             ₂₁Sc   [Ar]4s²3d¹ 

Notice the small differences between the two expressions above for the electron configuration of Scandium. This is something to be aware about.