Quantum Number Calculator

Quantum number calculator helps you determine the specific quantum numbers for electrons, including their energy levels, orbital shapes, and spin directions. It also calculates the number of orbitals, maximum electrons, and provides combinations of quantum numbers to better understand the electron’s behavior within the atomic structure.

What are Quantum Numbers?

Quantum numbers are the set of values that are used to describe the position and energy of an electron within an atom.

There are four main quantum numbers to describe the electron in an atom:

• Principal quantum number (n)
• Angular momentum quantum number (l)
• Magnetic quantum number (ml)
• Spin quantum number (ms)

These quantum numbers collectively create a unique identity for each electron inside an atom. They follow the Pauli Exclusion Principle, which states that two electrons within an atom can never have the same set of quantum numbers, as calculated by the quantum number calculator. 

Principal quantum number (n):

A principal quantum number is a positive number that defines the main electron’s shell or energy level in an atom and it is denoted by the symbol (n). 

The value of (n) is:

(n = 1, 2, 3, 4, …)

For instance:

When the principal quantum number is 1 (n = 1), this represents the first energy level or shell and is referred to as the K shell. Electrons in this innermost shell have the lowest energy and are closest to the nucleus.

Angular momentum quantum number (l):

The angular momentum quantum number describes the shape of an orbital and indicates which subshells are present in the principal shell.

It is also known as the secondary quantum number or azimuthal quantum number. It is denoted by the symbol (l) and it can vary from zero to n –1, such as:

l = 0,1,2,3,...,n −1

When l is given, the electron's orbital angular momentum magnitude (L) is expressed as:

\(L = \sqrt{l(l+1)} \frac{h}{2\pi}\)

For Example:

For an electron in the first energy level (n = 1), the possible values for the angular momentum quantum number (l) can be 0. When l = 0, it represents an s orbital with a spherical shape around the nucleus.

In the second energy level (n = 2), the angular momentum quantum number (l) can have values of 0 or 1. When l = 0, it corresponds to an s orbital, similar to the one in the first energy level. When l = 1, it represents a p orbital

In the following table, the names of orbitals corresponding to different values of (l) are listed.

Magnetic quantum number (ml):

Magnetic quantum numbers describe the orientation or direction of an electron's orbit within a specific orbital type (like s, p, d, f). They indicate the number of possible spatial orientations an electron can have within an orbital.

For instance, for a specific orbital shape (like a p orbital), the magnetic quantum number is what helps us distinguish the various directions or specific spots where an electron could be found within that orbital.

The possible values of (ml) for a given (l) are −l through 0 +l, such as:

ml =−l,−(l−1),...,0,...,(l−1),l

For Example:

let's take a p orbital as an example. For a p orbital, the magnetic quantum number (ml) can have values from -1 to 1, including 0.

These values indicate the different spatial orientations or positions where an electron could be situated within the p orbital along the three-dimensional axes (x, y, and z) in space. For instance:

• When m = -1: The electron tends to be mostly in one direction.
• When m = 0: It's centered along a different direction.
• When m = 1: It leans toward yet another direction.

Each value of the magnetic quantum number (m) represents a distinct orientation or spatial position within the specific shape of the orbital.

Spin quantum number (ms):

The spin quantum number is like a tiny property that electrons have. It indicated that if an electron is spinning clockwise or counter-clockwise as it moves around inside an atom. This property aids in distinguishing one electron from another within the atomic structure.

It only has two possible values: 

• +1/2 for spin-up, and
• -1/2 for spin down

Thus, the value of (ms) is,

ms = ±1/2

Depending on (ms), the spin angular momentum of electron S is as follows:

\(S = \sqrt{s(s+1)} \times \frac{h}{2\pi}\)