Electron Density and Orbital Shapes

Atomic orbitals are mathematical descriptions of where the electrons in an atom (or molecule) are most likely to be found. These descriptions are obtained by solving an equation known as the Schrödinger equation, which expresses our knowledge of the atomic world. As the angular momentum and energy of an electron increases, it tends to reside in differently shaped orbitals. The orbitals corresponding to the three lowest energy states are s, p, and d, respectively. The illustration shows the spatial distribution of electrons within these orbitals. The fundamental nature of electrons prevents more than two from ever being in the same orbital. The overall distribution of electrons in an atom is the sum of many such pictures. This description has been confirmed by many experiments in chemistry and physics, including an actual picture of a p-orbital made by a Scanning Tunneling Microscope.

Most of the physical and chemical properties of atoms, and hence of all matter, are determined by the nature of the electron cloud enclosing the nucleus.

The nucleus of an atom, with its positive electric charge, attracts negatively charged electrons. This attraction is largely responsible for holding the atom together. The revolution of electrons about a nucleus is determined by the force with which they are attracted to the nucleus. The electrons move very rapidly, and determination of exactly where any particular one is at a given time is theoretically impossible (see Uncertainty Principle). If the atom were visible, the electrons might appear as a cloud, or fog, that is dense in some spots, thin in others. The shape of this cloud and the probability of finding an electron at any point in the cloud can be calculated from the equations of wave mechanics (see Quantum Theory). The solutions of these equations are called orbitals. Each orbital is associated with a definite energy, and each may be occupied by no more than two electrons. If an orbital contains two electrons, the electrons must have opposite spins, a property related to the angular momentum of the electrons. The electrons occupy the orbitals of lowest energy first, then the orbitals next in energy, and so on, building out until the atom is complete (see Atom).

The orbitals tend to form groups known as shells (so-called because they are analogous to the layers, or shells, around an onion). Each shell is associated with a different level of energy. Starting from the nucleus and counting outward, the shells, or principal energy levels, are numbered 1, 2, 3, … , n. The outer shells have more space than the inner ones and can accommodate more orbitals and therefore more electrons. The nth shell consists of 2n-1 orbitals, and each orbital can hold a maximum of 2 electrons. For example, the third shell contains five orbitals and holds a maximum of 10 electrons; the fourth shell contains seven orbitals and holds a maximum of 14 electrons. Among the known elements, only the first seven shells of an atom contain electrons, and only the first four shells are ever filled.

Each shell (designated as n) contains different types of orbitals, numbered from 0 to n-1. The first four types of orbitals are known by their letter designations as s, p, d, and f. There is one s-orbital in each shell, and this orbital contains the most firmly bound electrons of the shell. The s-orbital is followed by the p-orbitals (which always occur in groups of three), the d-orbitals (which always occur in groups of five), and finally the f-orbitals (which always occur in groups of seven). The s-orbitals are always spherically shaped around the nucleus; each p-orbital has two lobes resembling two balls touching; each d-orbital has four lobes; and each f-orbital has eight lobes. The p-, d-, and f-orbitals have a directional orientation in space, but the spherical s-orbitals do not. The three p-orbitals are oriented perpendicular to one another along the axis of an imaginary three-dimensional Cartesian (x, y, z) coordinate system. The three p-orbitals are designated p_x, p_y, and p_z, respectively. The d- and f-orbitals are similarly arranged about the nucleus at fixed angles to one another.

When elements are listed in order of increasing atomic number, an atom of one element contains one more electron than an atom of the preceding element (see Chemical Elements). The added electrons fill orbitals in order of the increasing energy of the orbitals. The first shell contains the 1s orbital; the second shell contains the 2s orbital and the 2p orbitals; the third shell contains the 3s orbital, the 3p orbitals, and the 3d orbitals; the fourth shell contains the 4s orbital, the 4p orbitals, the 4d orbitals, and the 4f orbitals.

After the two innermost shells, certain orbitals of outer shells have lower energies than the last orbitals of preceding shells. For this reason, some orbitals of the outer shells fill before the previous shells are complete. For example, the s-orbital of the fourth shell (4s) fills before the d-orbitals of the third shell (3d). Orbitals generally fill in this order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.

In a notation frequently used to describe the electron configuration of an element, a superscript after the orbital letter gives the number of electrons in that orbital. Thus, 1s²2s²2p⁵ means that the atom has two electrons in the 1s orbital, two electrons in the 2s orbital, and five electrons in the 2p orbitals.

Neutral atoms with exactly eight electrons in the outer shell (meaning the s- and p-orbitals of the outer shell are filled) are exceptionally stable. These neutral atoms are atoms of the noble gases, which are so stable that getting them to chemically react with other elements is very difficult. The unusual stability of the noble-gas electron structures is of great importance in chemical bonding and reactivity. All other elements tend to combine with each other in such a way as to imitate this stable structure. The structure of helium is 1s²; neon adds another stable shell, 2s²2p⁶, to this; argon adds the orbitals 3s²3p⁶; krypton adds the orbitals 4s²3d¹⁰4p⁶; and xenon adds the orbitals 5s²4d¹⁰5p⁶ (the s-orbital fills before the d-orbital of the previous shell).