Quantum Numbers Lecture

Overview

• Schrodinger Equation: Provides wave function for electrons; helps determine location.
• Heisenberg Uncertainty Principle: Cannot know position and velocity of electron simultaneously with precision.
• Wave Function Squared: Yields probability density for electron location, describing orbitals.

Orbitals vs. Orbits

• Orbitals: Describe electron density distribution, not to be confused with Bohr's orbits.
• Characteristics: Energy and electron density distribution.

Quantum Numbers

• Used to describe electron arrangements in atoms.

1. Principal Quantum Number (n)

• Symbol: n
• Description: Describes electron shell (energy level) and size of orbital.
• Values: Positive integers (1 to ∞).
• Implications: Larger n means higher energy and electrons are further from nucleus.

2. Angular Momentum Quantum Number (L)

• Symbol: L
• Description: Describes shape of atomic orbital (subshell).
• Values: Integral values from 0 to n-1.
• Subshell Designations:
  • L = 0: s (sharp)
  • L = 1: p (principal)
  • L = 2: d (diffuse)
  • L = 3: f (fundamental)

3. Magnetic Quantum Number (M_L)

• Symbol: M_L
• Description: Describes orientation of orbital in 3D space.
• Values: Range from -L to +L, including 0.
• Example:
  • If L = 2, M_L can be -2, -1, 0, 1, 2.

4. Electron Spin Quantum Number (M_S)

• Symbol: M_S
• Description: Describes spin of electron.
• Values: -1/2 or +1/2.
• Significance: Explains splitting of spectral lines in magnetic fields.

Allowed Quantum Numbers for Energy Levels

• n = 1: Only 1s (M_L = 0)
• n = 2: 2s (M_L = 0), 2p (M_L = -1, 0, 1)
• n = 3: 3s (M_L = 0), 3p (M_L = -1, 0, 1), 3d (M_L = -2, -1, 0, 1, 2)
• n = 4: 4s, 4p, 4d, 4f; M_L ranges from -3 to 3

Total Number of Orbitals in Shells

• Formula: Number of orbitals = n²
• Examples:
  • n = 1: 1² = 1 orbital
  • n = 2: 2² = 4 orbitals
  • n = 3: 3² = 9 orbitals
  • n = 4: 4² = 16 orbitals

Exploration of Fifth Energy Level (n=5)

• L Values: 0 to 4
• Letter Designations:
  • 5s, 5p, 5d, 5f, 5g
• Magnetic Quantum Numbers:
  • 5s: M_L = 0
  • 5p: M_L = -1, 0, 1
  • 5d: M_L = -2, -1, 0, 1, 2
  • 5f: M_L = -3 to 3
  • 5g: M_L = -4 to 4

Participation Question

• Task: Identify which sets of quantum numbers are not allowed based on the rules discussed.

Conclusion

• Quantum numbers: Critical for describing electron arrangements in atoms.
• Review: Principal quantum number for shell, angular momentum for subshell shape, magnetic number for orientation, and spin number for electron spin.