# Electron Orbitals

According to quantum mechanics, electrons do not move around the nucleus in a defined circular orbit, like the Bohr model. Given the limitations of the Heisenberg principle, we do not actually know how the electron is moving. The wave function gives us no information about the detailed pathway of the electron. We cannot predict the motion of an electron. We can only think of the electron in terms of probability. The square of the wave function indicates the probability of finding an electron near a particular point in space. The best way to illustrate the square of the wave function is a probability distribution. The probability of finding an electron at a particular position is greatest close to the nucleus and it becomes less probable as the distance from the nucleus increases.

Thus, we can not give a precise definition of the size of an electron orbital. The probability of finding the electron at any point in space is never zero, therefore, an orbital has no distinct size. An electron orbital is most commonly defined as the radius of the sphere that encloses 90% of the total electron probability.

QUANTUM NUMBERS

Each orbital can be characterized by a series of numbers called quantum numbers. According to the Pauli Exclusion Principle, no two electrons can have the same set of four quantum numbers.

The principal quantum number (n) has integral values: 1, 2, 3... The principal quantum number is related to the size and energy of the orbital. As n increases, the orbital become larger. It also has a higher energy, because the electron is less tightly bound to the nucleus. The smallest average distance and the lowest energy occurs when n = 1.

The angular momentum quantum number (l) has integral values from 0 to n - 1 for each value of n. This quantum number is related to the shape of the atomic orbitals. The values of l is commonly assigned a letter [values = 0 (for s), 1(for p), 2 (for d), 3 (for f) sub levels].

The magnetic quantum number (ml) has integral values between l and -l, including zero. This quantum number is related to the orientation of the orbitals in space relative to the other orbitals in the atom.

The electron spin quantum number (m s) represents the electron spin. The electron can spin in one of two opposite directions, and thus has only two possible values: + 1/2 and - 1/2.

S Orbitals

Each principal quantum level has an s orbital. The s orbital corresponds to the l value of 0. As there is only one s orbital per principal quantum level, there is only one possible value of ml: 0.

P Orbitals

P orbitals are present in principal quantum levels of 2 and beyond. The p orbitals correspond to the l value of 1. As there are three different orientations of the p orbitals (x,y, and z), there are three possible values of ml: -1, 0, +1.

D Orbitals

D orbitals are present in principal quantum levels of 3 and beyond. The p orbitals correspond to the l value of 2. As there are five different orientations of the d orbitals, there are five possible values of ml: -2, -1, 0, +1, +2.

F Orbitals

F orbitals are present in principal quantum levels of 4 and beyond. The p orbitals correspond to the l value of 3. As there are seven different orientations of the f orbitals, there are seven possible values of ml: -3, -2, -1, 0, +1, +2, +3.