Overview
This lecture covers the four quantum numbers used to describe the unique position and properties of electrons in atoms, explaining how each number is determined and their relationships.
Principal Quantum Number (n)
- The principal quantum number (n) indicates the energy level of an electron and is a positive integer (1, 2, 3, ...).
- n determines the main shell in which an electron resides.
Angular Momentum Quantum Number (l)
- The angular momentum quantum number (l) describes the shape of the sublevel (subshell) and depends on n: l = 0 to n-1.
- Sublevel types: s (l=0), p (l=1), d (l=2), f (l=3).
- The allowed sublevels for each n:
- n=1: only s
- n=2: s, p
- n=3: s, p, d
- n=4: s, p, d, f
Magnetic Quantum Number (ml)
- The magnetic quantum number (ml) specifies the orientation of orbitals within a sublevel: ml ranges from -l to +l in integer steps.
- Number of orbitals per sublevel:
- s (l=0): 1 orbital (ml=0)
- p (l=1): 3 orbitals (ml=-1, 0, +1)
- d (l=2): 5 orbitals (ml=-2 to +2)
- f (l=3): 7 orbitals (ml=-3 to +3)
Electron Spin Quantum Number (ms)
- The electron spin quantum number (ms) describes the spin direction of the electron: +½ (up) or –½ (down).
- Each orbital can hold two electrons with opposite spins.
Assigning Quantum Numbers to Electrons
- The four quantum numbers uniquely describe a specific electron.
- Example: For the 3d sublevel, n=3, l=2, ml can be -2, -1, 0, +1, +2; ms = +½ or -½.
- The specific values depend on the order electrons fill the orbitals and their spins.
Key Terms & Definitions
- Principal Quantum Number (n) — integer representing the main energy level.
- Angular Momentum Quantum Number (l) — integer (0 to n-1) indicating sublevel shape.
- Magnetic Quantum Number (ml) — integer (-l to +l) specifying orbital orientation.
- Electron Spin Quantum Number (ms) — spin of electron, either +½ or –½.
- Sublevel — subdivision of a main energy level (s, p, d, f).
- Orbital — region where the probability of finding an electron is high.
Action Items / Next Steps
- Review the sublevel and quantum number relationships for each energy level.
- Practice assigning all four quantum numbers for different electrons in various elements.
- Consult additional resources and practice problems on quantum numbers and electron configurations if needed.