Quantum Numbers and Orbitals
The four quantum numbers n, l, m and s specify the energy, shape, orientation and spin state of an electron in an atom.
What is Quantum Numbers and Orbitals?
The four quantum numbers n, l, m and s specify the energy, shape, orientation and spin state of an electron in an atom.
Key formula / rule: l ranges from 0 to n-1 and m from -l to +l.
Key points
- Identify the permitted sets of quantum numbers for an electron.
- Derive the number of orbitals and electrons in a given shell.
Common exam trap
Allowing l to equal n.
Definitions
- Term
Quantum Numbers and Orbitals
- Meaning
The four quantum numbers n, l, m and s specify the energy, shape, orientation and spin state of an electron in an atom.
- Term
Quantum Numbers and Orbitals — explanation
- Meaning
Each orbital is defined by a unique n, l, m triple and holds at most two electrons of opposite spin. Orbital shapes follow from l, which is why d orbitals appear only from n = 3 onwards.
Learning objectives
Identify the permitted sets of quantum numbers for an electron.
Derive the number of orbitals and electrons in a given shell.
Formulae
- Key point
l ranges from 0 to n-1 and m from -l to +l.
- Key point
Each orbital holds a maximum of two electrons with opposite spins.
- Key point
The number of radial nodes is n - l - 1.
Prerequisites
CHE-U1-BC-T2-S1-C1
Common mistakes
Allowing l to equal n.
Confusing the number of orbitals in a subshell with the number of electrons.
Keywords
Quantum
Numbers
Orbitals
Practice preview
How many orbitals are present in the third principal energy level (n=3)?…
easy
What are the possible values for the magnetic quantum number (m) for an electron in a 'd' subshell?…
medium
Which of the following sets of quantum numbers (n, l, m, s) is NOT possible for an electron in an atom?…
medium