Quantum Numbers

Quantum Number

A solution to the Schrodinger equation that specifies the properties of an atomic orbital and the electrons found in that orbital.

Principle Quantum # (symbol)

n

Angular Momentum Quantum # (symbol)

l

Magnetic Quantum # (symbol)

m

Spin Quantum # (symbol)

s

Principle Quantum # (definition)

Indicates the main energy level occupied by the electron.

Angular Momentum Quantum # (definition)

Indicates the shape of the orbital.

Magnetic Quantum # (definition)

Indicates the orientation of an orbital around the nucleus.

Spin Quantum # (definition)

Indicates the direction an electron rotates in its orbital.

What are the allowable values for n?

Any positive integer, from 1 to n.

What are the allowable values for l?

Any positive integer in the range [0, ..., n-1].

What are the allowable values for m?

Any integer in the range [-l, ..., +l].

What are the allowable values for s?

-1/2 and +1/2 only.

Orbital

A three-dimensional region around a nucleus that indicates the probable location of an electron, defined by specific values of n, l, and m.

Sublevel/Subshell

All similarly shaped orbitals that share the same values for n and l.

Energy Level/Shell

All orbitals that share the same value for n only.

s-orbital

A spherical orbital defined by l=0

p-orbital

A dumbbell-shaped orbital defined by l=1

d-orbital

A cloverleaf-shaped orbital defined by l=2

f-orbital

A complex orbital defined by l=3