## What is an Electron Orbital?

**Electron orbitals** are mathematical functions that describe the probability of finding an electron around the nucleus of an atom. Each orbital can hold two electrons. They are also known as atomic orbitals. Atomic orbitals come in different shapes, depending on how much energy and angular momentum is associated with that orbital. We will learn about the shapes of s, p, d, and f orbitals.

The precise **definition **of an orbital, is a complex valued mathematical function that describes probability density of the location of an electron in an atom.

Degenerate orbitals are orbitals in the same main energy level and sublevel that have different orientations. For example, the 5 d-orbitals, shown below, are degenerate orbitals.

## Basic Review of the Quantum Numbers

For more details on the quantum numbers, check out our quantum numbers article! There are four quantum numbers that tell the energy level, shape, orientation, and spin of an electron.

- Principal Quantum Number (
*n*): indicates main energy level of an electron. The higher the principal quantum number is, the higher the energy level. - Angular Momentum Quantum Number (
*l*): indicates the shape of an orbital. Different values of*l*correspond to specific shapes of electron orbitals. This will be discussed more in detail later. This quantum number is where s, p, d, and f orbitals come from. - Magnetic Quantum Number (
*m*): indicates the orientation of an orbital around the nucleus. - Spin Quantum Number: indicates whether an electron is ‘spin up’ or ‘spin down’. There are a maximum of two electrons per orbital, and if they both reside in the orbital, they must be spinning the opposite directions (meaning they have the opposite spin quantum number).

## Angular Momentum Quantum Number & Orbital Shapes

The angular momentum quantum number has integer values from 0 to (*n*-1). So, if the principal quantum number (*n*) = 4, the angular momentum quantum numbers are 0, 1, 2, and 3.

Each angular momentum quantum number represents a letter, which corresponds to a specific shape of an orbital. As you can see, the higher the principal quantum number, the higher the angular momentum quantum number, and the more complex the orbital shape becomes. Complexity comes from the number of lobes in an orbital, and the number and types of nodes an orbital has. A node is a part of an orbital where the wavefunction is zero. p orbitals have planar nodes between their two lobes.

Principal Quantum # (n) | Angular Momentum Quantum # (l) | Letter | Orbital Shape Diagram |

1 | 0 | s | |

2 | 1 | p | |

3 | 2 | d | |

4 | 3 | f |

## How Do Electrons Occupy the Orbital Space?

### S Orbital

At the first main energy level, when n = 1, the only sublevel, or orbital, possible is the s-orbital, which has a sphere shape.

### P Orbital

When n = 2, two sublevels are possible: these are the s-orbital and p-orbitals. If you recall, the magnetic quantum number shows the orientations of an orbital, with the values –*l* to +*l*. So an s-orbital has only one magnetic quantum number which is 1, meaning it only has one possible orientation. This makes sense because a sphere has the same shape no matter how it is rotated. Thus, a p-orbital has three possible orientations (-1, 0, 1 magnetic quantum numbers).

Neon, the last element in the main second energy level, has 10 electrons. How are these electrons distributed and located? The first 2 electrons go in the 1s-orbital, or the s-orbital in the first main energy level. Then, the next 2 electrons occupy in the 2s-orbital, or the s-orbital in the second main energy level. Remember, because there is only one orientation of an s-orbital, there is only one s-orbital per energy level. Finally, the last 6 electrons are divided evenly into the 2p-orbitals. Since there are three orientations of a p-orbital, there are three p-orbitals per energy level.

As shown in the example above, electrons can be identified by the orbitals in which they reside. Electron configurations show how electrons are organized in orbitals in an atom.

## Learn More

Check out some of our other related articles!