Lecture on Quantum Numbers and Electron Configuration

Introduction to Orbitals

• Orbital: Most probable location to find an electron.
• Using the Bohr model, orbits are circular paths around the nucleus.
• Energy Levels (n):
  • First energy level: n = 1
  • Second energy level: n = 2
  • Third energy level: n = 3
  • Higher n means higher energy and further distance from the nucleus.
  • Principal Quantum Number (n) describes the size and energy of orbitals.

Quantum Numbers

1. Principal Quantum Number (n)
   • Indicates energy level or shell.
   • Higher n = further from the nucleus = higher energy level.
2. Angular Momentum Quantum Number (L)
   • Describes shape of the orbital.
   • L = 0: s orbital (spherical)
   • L = 1: p orbital (dumbbell-shaped)
   • L = 2: d orbital (cloverleaf)
   • L = 3: f orbital (complex shape)
   • L determines sub-levels/shells in a given n.

Sub-levels and Relationship between n and L

• L is always less than or equal to n-1.
• Examples:
  • n = 1: L = 0 (s sub-level only)
  • n = 2: L = 0, 1 (s and p sub-levels)
  • n = 3: L = 0, 1, 2 (s, p, and d sub-levels)
  • n = 4: L = 0, 1, 2, 3 (s, p, d, and f sub-levels)
• Number of sub-levels = n.

Magnetic Quantum Number (M sub L)

• Describes the orientation of the orbital.
• For any given L, ML ranges from -L to +L.
  • Example:
    • L = 0 (s), ML = 0 (1 orbital)
    • L = 1 (p), ML = -1, 0, +1 (3 orbitals: Px, Py, Pz)
    • L = 2 (d), ML = -2, -1, 0, +1, +2 (5 orbitals)

Electron Spin Quantum Number (M sub S)

• Indicates electron spin direction.
• Possible values: +1/2 (up spin) or -1/2 (down spin).
• Pauli's Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

Examples

• 2p5 Electron:

  • n = 2 (second energy level)
  • L = 1 (p sub-level)
  • ML = 0 (fifth electron in p sub-level)
  • MS = -1/2 (down spin)

• 3d5 Electron:

  • n = 3 (third energy level)
  • L = 2 (d sub-level)
  • ML = 2 (fifth electron)
  • MS = +1/2 (up spin)

Conclusion

• Quantum numbers help uniquely identify the position and state of an electron in an atom.
• For more examples and detailed explanations, refer to further resources available in chemistry video playlists.