The document discusses the four quantum numbers used to describe electrons in an atom: 1) The principal quantum number (n) indicates the electron shell and energy level of an electron. Higher n corresponds to higher energy levels further from the nucleus. 2) The azimuthal quantum number (l) indicates the subshell shape (s, p, d, f) and relates to the orbital angular momentum. 3) The magnetic quantum number (ml) indicates the orientation of orbitals within a subshell and can have values from -l to +l. 4) The spin quantum number (ms) describes the spin of an electron as +1/2 or -1/2, allowing a maximum of two

1. QUANTUM NUMBER
Edited by → Waseem Ahmed Bhatti (M.Sc Chemistry)
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2. Quantum Number
▪ Principal Quantum Number → denoted by (n)
▪ Azimuthal Quantum Number → denoted by (l)
▪ Magnetic Quantum Number → denoted by (ml)
▪ Spin Quantum Number → denoted by (ms)
We used these parameter for identity and location of electrons or
address of electrons.

3. Principal Quantum Number (n)
- Distance from nucleus (Size)
- Energy of an electron
n → 1,2,3,4,5 ……. so on
The value of principal quantum positive integer
↓ ↓ ↓ ↓ ↓
This principal quantum number given information about shell of an
atom.

4. Subshells
Same n → Same shell
Subshell Shape
▪ s ▪ Spherical
▪ p ▪ collection of dumb-bell
▪ d ▪ collection of double dumb-bell
▪ F ▪ ---------------------------------

5. Azimuthal Quantum Number (l)
• s • l = 0 • n = 1 • 1s0
• p • l = 1 • n = 2 • 2s0 2p1
• d • l = 2 • n = 3 • 3s0 3p1 3d2
• f • l = 3 • n = 4 • 4s0 4p1 4d2 4f3
l = 0 - n = 1
l = 1 - n = 2
l = 2 - n = 3
l = 3 - n = 4
→ Shape
→ Energy

6. Orbitals & Orientation
➢ p Orbitals
• x-axis oriented
• y-axis oriented →
• Z-axis oriented
➢ d Orbital
• xy-axis oriented
• xz-axis oriented
• yz-axis oriented →
• x2 – y2 - axis oriented
• z2 – axis oriented

7. Magnetic Quantum Number (m)
• l • Subshell • Orientation • ml
• 0 • s n = 1 • 1 • 0
• 1 • p n = 2 • 3 (px py pz) • -1, 0, +1
• 2 • d n = 3 • 5 (dxy dxz dyz dx2-y2 dz2) • -2, -1, 0, +1, +2
• 3 • f n = 4 • ----------------------------------- • -3, -2, -1, 0, +1, +2, +3
ml → -l, 0, +l

8. Degenerate Orbitals
3px
3py
3pz
→ n = 3
→ l = 1
5dxy
5dxz
5dyz
5dx2-y2
5dz2
→ n = 5
→ l = 2
n,l identical
Energy identical

9. Spin Quantum Number (ms)
Each orbital can accommodate maximum of 2
electrons
• Opposite spins ms
• ↻ +½ clockwise
• ↺ -½ anti clockwise