Quantum numbers

Definition

Quantum numbers are sets of numerical values that describe the unique quantum state of an electron in an atom. They provide information about the electron’s energy level, orbital shape, orbital orientation, and spin direction.

5 Must Know Facts For Your Next Test

1. The four types of quantum numbers are principal ($n$), azimuthal ($l$), magnetic ($m_l$), and spin ($m_s$).
2. The principal quantum number ($n$) determines the energy level and size of the orbital.
3. The azimuthal quantum number ($l$) determines the shape of the orbital and ranges from 0 to $n-1$.
4. The magnetic quantum number ($m_l$) determines the orientation of the orbital in space and ranges from $-l$ to $+l$.
5. The spin quantum number ($m_s$) describes the intrinsic spin of the electron and can be either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Review Questions

• What does each type of quantum number represent?
• How do you determine the possible values for the azimuthal quantum number given a principal quantum number?
• What are the possible values for a magnetic quantum number if $l = 2$?

Related terms

Orbital: A region in an atom where there is a high probability of finding electrons.

Pauli Exclusion Principle:

A principle stating that no two electrons in an atom can have identical sets of all four quantum numbers.

Electron Configuration:

The distribution of electrons among orbitals in an atom or molecule.