# How Quantum Numbers Relate to the Features of an Orbital

An orbital is a region of space where an electron in an atom is most likely to be found. The shape, size, and orientation of an orbital are determined by three quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml). In this article, we will explore what feature of an orbital is related to each of these quantum numbers.

### The Principal Quantum Number (n)

The principal quantum number (n) is the most important quantum number because it determines the energy level of an electron in an atom. The value of n can be any positive integer, such as 1, 2, 3, and so on. The higher the value of n, the higher the energy level and the farther the orbital is from the nucleus. For example, an electron in the n = 1 orbital has the lowest energy and is closest to the nucleus, while an electron in the n = 4 orbital has a higher energy and is farther away from the nucleus.

The principal quantum number also determines the number of subshells within a shell. A shell is a group of orbitals that have the same value of n. A subshell is a group of orbitals that have the same values of n and l. The number of subshells in a shell is equal to n. For example, the n = 2 shell has two subshells: one with l = 0 and one with l = 1. The n = 3 shell has three subshells: one with l = 0, one with l = 1, and one with l = 2.

### The Azimuthal Quantum Number (l)

The azimuthal quantum number (l) describes the shape of the orbital. The value of l depends on the value of n and can range from 0 to n – 1. For example, if n = 2, l can be either 0 or 1. If n = 3, l can be either 0, 1, or 2.

The value of l also determines the type of orbital. Each value of l corresponds to a letter that represents a different type of orbital: s, p, d, f, and so on. For example, if l = 0, the orbital is called an s orbital. If l = 1, the orbital is called a p orbital. If l = 2, the orbital is called a d orbital. The shape of these orbitals can be visualized as follows:

• An s orbital has a spherical shape and can hold up to two electrons.
• A p orbital has a dumbbell shape and can hold up to six electrons.
• A d orbital has a cloverleaf shape and can hold up to ten electrons.

The azimuthal quantum number also determines the number of orbitals within a subshell. The number of orbitals in a subshell is equal to 2l + 1. For example, if l = 0, there is only one orbital in the subshell. If l = 1, there are three orbitals in the subshell. If l = 2, there are five orbitals in the subshell.

### The Magnetic Quantum Number (ml)

The magnetic quantum number (ml) describes the orientation of the orbital in space relative to an applied magnetic field. The value of ml depends on the value of l and can range from -l to +l in integer steps. For example, if l = 0, ml can only be 0. If l = 1, ml can be -1, 0, or +1. If l = 2, ml can be -2, -1, 0, +1, or +2.

The value of ml also determines which axis or plane the orbital lies along or between. For example:

• If ml = 0, the orbital lies along or contains the z-axis.
• If ml = +1 or -1, the orbital lies between or contains the x-axis and y-axis.
• If ml = +2 or -2, the orbital lies between or contains two diagonal axes.

The magnetic quantum number also determines how many electrons can occupy an orbital with a given orientation. According to Pauli’s exclusion principle, no two electrons in an atom can have the same set of four quantum numbers (n, l, ml, and ms). Therefore, each orbital can hold up to two electrons with opposite spins.

## Conclusion

In summary, quantum numbers are used to describe the features of an orbital in an atom. The principal quantum number (n) relates to the energy level and size of the orbital. The azimuthal quantum number (l) relates to the shape and type of the orbital. The magnetic quantum number (ml) relates to the orientation and axis of the orbital. By knowing these quantum numbers, we can understand how electrons are distributed in atoms and how they interact with each other and with external fields.