General Chemistry/Shells and Orbitals

Electron shells

Each different shell is subdivided into one or more orbitals, each of which has a different angular momentum. Each orbital in a shell has a characteristic shape, and are named by a letter. They are: s, p, d, and f. (which stands for Sharp, principle, diffuse, and fundamental respectively and refer to lines seen in spectroscopy). In a one electron atom (e.g H, He⁺, Li⁺⁺ etc.) the energy of each of the orbitals within a particular shell are all identical. However when there is more than one electron, they interact with one another and split the orbitals into slightly different energies. Within any particular shell, the energy of the orbitals depends on the angular momentum, with the s orbital having the lowest energy, then p, then d, etc.

The S Orbital

Atomic 1s orbitals
Stylised image of the 1s atomic orbital.

The simplest orbital in the atom is the 1s orbital. It has no radial or angular nodes: the 1s orbital is simply a sphere of electron density. As with all orbitals the number of radial nodes increases with the principle quantum number (i.e. the 2s orbital has one radial node, the 3s has two etc.). Because the angular momentum quantum number is 0, there is only one choice for the magnetic quantum number - there is only one s orbital per shell. The s orbital can hold two electrons, as long as they have different spin quantum numbers.

$\begin{matrix} l & = & 0 \\ m_{l} & = & 0 \\ m_{s} & = & + \frac{1}{2}, - \frac{1}{2} \end{matrix}$

The P Orbitals

Stylised image of all the 2p atomic orbitals.

Starting from the 2nd shell, there is a set of p orbitals. The angular momentum quantum number of the electrons confined to p orbitals is 1, so each orbital has one angular node. There are 3 choices for the magnetic quantum number, which indicates 3 differently orientated p orbitals. Finally, each orbital can accomodate two electrons (with opposite spins), giving the p orbitals a total capacity of 6 electrons.

$\begin{matrix} l & = & 1 \\ m_{l} & = & - 1, 0, 1 \\ m_{s} & = & + \frac{1}{2}, - \frac{1}{2} \end{matrix}$

The p orbitals all have two lobes of electron density pointing along each of the axes. Each one is symmetrical along its axis. The notation for the p orbitals indicate which axis it points down, i.e. p_x points along the x axis, p_y on the y axis and p_z up and down the z axis. The p orbitals are degenerate, they all have the same energy. P orbitals are very often involved in bonding.

2p_x	2p_y	2p_z

The D Orbitals

Stylised image of all the 3d atomic orbitals.

The first set of d orbitals is the 3d set. The angular momentum quantum number is 2, so each orbital has two angular nodes. There are 5 choices for the magnetic quantum number, which gives rise to 5 different d orbitals. Each orbital can hold two electrons (with opposite spins), giving the d orbitals a total capacity of 10 electrons.

$\begin{matrix} l & = & 2 \\ m_{l} & = & - 2, - 1, 0, 1, 2 \\ m_{s} & = & + \frac{1}{2}, - \frac{1}{2} \end{matrix}$

Note that all the d orbitals have four lobes of electron density, except for the d_z2 orbital, which has two opposing lobes and a doughnut of electron density around the middle. The d orbitals can be further subdivided into two smaller sets. The d_x2-y2 and d_z2 all point directly along the x, y and z axis they form an e_g set. On the other hand the lobes of the d_xy, d_xz and d_yz all line in the quadrants, with no electron density on the axis. These three orbitals form the t_2g set. In most cases, the d orbitals are degenerate, but sometimes, they can split, with the e_g and t_2g subsets having different energy. Crystal Field Theory predicts and accounts for this. D orbitals are sometimes involved in bonding, especially in inorganic chemistry.