Quantum Numbers and Electron Configuration

Introduction to Quantum Numbers

• Electrons are both particles and waves.
• The arrangement of electrons in an atom is described by 4 quantum numbers.
• Orbitals: Regions of probability where electrons can be found. Types of orbitals: s, p, d, f.
  • Each orbital can hold up to 2 electrons.
  • More electrons require more orbitals.

Quantum Numbers Explained

1. Principal Quantum Number (n)

• Represents energy levels of electrons.
• Can have any positive integer value.
• Larger n means further from the nucleus.

2. Angular Momentum Quantum Number (l)

• Can have values from 0 to n-1.
  • For example, if n=3, l can be 0, 1, or 2.
• Describes the shape of the orbital:
  • l=0: s orbitals (spherical, 1 per energy level)
  • l=1: p orbitals (three lobes, 3 per energy level)
  • l=2: d orbitals (five unique shapes, 5 per energy level)
  • l=3: f orbitals (seven unique shapes, 7 per energy level)

3. Magnetic Quantum Number (m_l)

• Values range from -l to +l.
• Determines how many orbitals of a type per energy level:
  • l=0: m_l=0 (1 s orbital)
  • l=1: m_l can be -1, 0, 1 (3 p orbitals)
  • l=2: m_l can be -2, -1, 0, 1, 2 (5 d orbitals)
  • l=3: m_l can be -3, -2, -1, 0, 1, 2, 3 (7 f orbitals)

4. Spin Quantum Number (m_s)

• Can be either +1/2 or -1/2.
• Each electron has a unique set of quantum numbers.
• Pauli exclusion principle: No two electrons can have the same set of 4 quantum numbers.

Examples of Quantum Numbers

• n=1: l=0, m_l=0 ➔ 1s orbital (2 electrons)
• n=2: l=0 ➔ 2s; l=1 ➔ 2p orbitals (can hold 8 electrons total)
• n=3: l=0 ➔ 3s; l=1 ➔ 3p; l=2 ➔ 3d orbitals.

Filling Orbitals and Electron Configuration

Aufbau Principle

• Order of filling is based on energy levels:
  1. 1s
  2. 2s
  3. 2p
  4. 3s
  5. 3p
• Example: Chlorine (17 electrons)
  • Fill 1s (2), 2s (2), 2p (6), 3s (2), 3p (5) ➔ Configuration: 1s² 2s² 2p⁶ 3s² 3p⁵.

Using the Periodic Table for Configurations

• Areas of the periodic table correspond to types of orbitals:
  • s block, p block, d block, f block.
• Travel left to right and up to down to get to an element's configuration.

Noble Gas Notation

• Abbreviation with noble gas from the previous row in brackets.
• For chlorine: [Ne] 3s² 3p⁵.

Orbital Diagrams

• Visual depiction of filled orbitals.
• Remember Hund's rule: Fill each orbital halfway before pairing.

Magnetic Properties

• Paramagnetic: Atoms with unpaired electrons; attracted by a magnetic field.
• Diamagnetic: Atoms with all paired electrons; not affected by a magnetic field.

Summary

• n: Energy level
• l: Type of orbital
• m_l: Specific orbital within a set
• m_s: Electron spin
• Aufbau principle guides electron filling based on energy levels.

• If confused, review lecture again for clarity.
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