Quantum Number Calculator

What Are Quantum Numbers?

Quantum numbers describe each electron in an atom. They define the shell, subshell shape, orbital orientation, and spin. No two electrons in an atom share the same full set of four numbers, which is Pauli's exclusion principle.

The Four Quantum Numbers

The principal quantum number \(n = 1, 2, 3, \ldots\) sets the main energy shell. The azimuthal quantum number \(l = 0, 1, \ldots, n-1\) defines subshell shape (s, p, d, f). The magnetic quantum number \(m_l = -l, \ldots, +l\) gives orbital orientation. Spin quantum number \(m_s = \pm 1/2\) describes electron spin.

Orbital notation like 3p² means shell \(n = 3\), p subshell (\(l = 1\)), with two electrons. Electrons fill degenerate orbitals singly with parallel spins before pairing (Hund's rule).

Frequently Asked Questions

What does 3p2 mean?

It means two electrons in the third shell p subshell. Principal n = 3, azimuthal l = 1, and two electrons occupy separate p orbitals with parallel spins.

How many electrons fit in a p subshell?

A p subshell has three orbitals (m_l = −1, 0, +1), each holding two electrons with opposite spin. Maximum capacity is six electrons.

What is the azimuthal quantum number for d orbitals?

d orbitals have l = 2. Allowed m_l values are −2, −1, 0, +1, and +2, giving five d orbitals and ten electron capacity.

Why can m_s only be plus or minus one half?

Electrons are spin-1/2 fermions. Measurement along any axis yields only two outcomes, conventionally written as +1/2 and −1/2.

What is Pauli's exclusion principle?

No two electrons in an atom may have identical values of n, l, m_l, and m_s. This limits each orbital to two electrons with opposite spins.

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What Are Quantum Numbers?

The Four Quantum Numbers

Frequently Asked Questions

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