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Quantum Numbers and Orbitals

Jun 11, 2025

Overview

This lecture explains orbitals, energy levels, sub-levels, quantum numbers, and how they describe the arrangement and properties of electrons in an atom.

Orbitals & Energy Levels

  • An orbital is the most probable location to find an electron.
  • In the Bohr model, energy levels are labeled by the principal quantum number (n).
  • As n increases, energy and distance from the nucleus also increase.
  • Electrons closer to the nucleus have lower energy.

Quantum Numbers

  • The principal quantum number (n) defines the energy level and size of the orbital.
  • The angular momentum quantum number (l) describes the shape of the orbital: s (sphere, l=0), p (dumbbell, l=1), d (clover, l=2), f (complex, l=3).
  • l can be any integer from 0 up to n-1.
  • The number of sub-levels in an energy level equals the value of n.

Sub-levels and their Types

  • For n=1: Only l=0 (s sublevel).
  • For n=2: l=0 (s) and l=1 (p).
  • For n=3: l=0 (s), l=1 (p), l=2 (d).
  • For n=4: l=0 (s), l=1 (p), l=2 (d), l=3 (f).

Orbitals within Sub-levels

  • The magnetic quantum number (ml) describes the orientation of orbitals.
  • ml ranges from ā€“l to +l for each sublevel.
  • s sublevel (l=0): 1 orbital (ml=0).
  • p sublevel (l=1): 3 orbitals (ml=ā€“1, 0, 1).
  • d sublevel (l=2): 5 orbitals (ml=ā€“2, ā€“1, 0, 1, 2).

Electron Spin

  • The spin quantum number (ms) describes electron spin direction: +Ā½ (up) or ā€“Ā½ (down).
  • Each orbital can hold two electrons with opposite spins.
  • Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

Examples of Quantum Numbers

  • For the 2pāµ electron: n=2, l=1, ml=0, ms=ā€“Ā½.
  • For the 3dāµ electron: n=3, l=2, ml=2, ms=+Ā½.

Key Terms & Definitions

  • Orbital ā€” Region with highest probability of finding an electron.
  • Principal Quantum Number (n) ā€” Indicates energy level and size of orbital.
  • Angular Momentum Quantum Number (l) ā€” Indicates shape of orbital.
  • Magnetic Quantum Number (ml) ā€” Indicates orientation of orbital.
  • Spin Quantum Number (ms) ā€” Indicates spin direction of electron.

Action Items / Next Steps

  • Practice assigning quantum numbers to electrons in given configurations.
  • Review additional chemistry video resources for more examples on quantum numbers and electron configurations.

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