Quantum numbers
We don’t know for sure where an electron is at any given point in time. Electrons occupy orbitals; the orbitals are inside energy sublevels, which themselves are inside energy levels. This orbital, or electron cloud, is a region in which there is a high probability of finding the electron. The orbital only tells us the probability of finding the electron at a particular location—it says nothing about the path travelled by the electron.
There are four quantum numbers that we use designate an electron. Each electron in an atom is uniquely described by four values for these numbers:
- principal ($n$)
- a positive integer representing the electron’s energy level
- azimuthal ($l$)
- a nonnegative integer from zero to $n-1$ describing shape of the orbital and identifying the sublevel within the energy level; commonly denoted by letters s, p, d, and f for the values 0, 1, 2, and 3, respectively
- magnetic (${m}_{l}$)
- an integer from $-l$ to $+l$ representing the orientation of the orbital
- spin (${m}_{s}$)
- either −½ or +½, representing the direction of the electron’s spin
All four numbers identify one electron. The first three identify an orbital, which contains up to 2 electrons. The first two identify the energy level and sublevel, which contains up to $2l+1$ orbitals each containing up to 2 electrons. The principal quantum number alone identifies the main energy level, which contains up to $2{n}^{2}$ electrons in total.
There are three rules about filling up electron orbitals:
- Aufbau principle
- fill lower energy levels ($n$) before moving on to the next energy level
- Pauli’s exclusion principle
- no two electrons have the same four quantum numbers
- Hund’s rule
- put one electron by itself in each orbital of a sublevel before making pairs
See pages 186–191 of the textbook to learn how to draw energy level diagrams. See pages 192–193 to learn about electron configuration.