Atomic Orbitals

Understanding Atomic Models

Bohr Model: An early model of atomic structure illustrating electrons moving in fixed orbits around the nucleus.

• Limitations:

  • Did not account for the emission spectra of elements more complex than hydrogen.
  • Neglected the wave-like properties of electrons.

• Introduction of Wave-Particle Duality:

  • The quantum mechanical model extends this understanding by introducing probabilistic wave functions instead of fixed paths.

• Wave-Particle Duality:

  • Reveals a dual nature of electrons, focusing on probabilistic views rather than deterministic ones.

• Uncertainty Principle:

  • Asserts that it is impossible to precisely determine both the position and momentum of an electron simultaneously.
  chatImportant

  This principle signifies a major shift from definite pathways to probabilistic insights in quantum mechanics.

Introduction to Atomic Orbitals

• Atomic Orbitals: Spaces with a high probability of locating electrons, as opposed to fixed trajectories.

• Wave Properties:

  • Example: Electron diffraction showcases the wave nature of electrons.

Principal Quantum Numbers

• Principal Quantum Number (n): Specifies the size and energy level of an orbital.

• Azimuthal Quantum Number (l): Indicates the shape of an orbital.

  

• Magnetic Quantum Number ($m_l$): Specifies the spatial orientation of orbitals.

• Spin Quantum Number ($m_s$): Identifies the spin direction of an electron.

  chatImportant

  Quantum numbers unlock insights into atomic behaviour, providing a deeper understanding of electron properties and behaviours.

Types of Orbitals

• s Orbitals: Spherical in shape and present in all energy levels.

  

• p Orbitals: Shaped like a dumbbell, with directional characteristics.

• d Orbitals: Feature complex shapes, influence properties such as colour.

• f Orbitals: Have intricate shapes, utilised in applications such as LED technology.

Electron Configuration

Electron Configuration: The distribution of electrons among atomic orbitals.

• Aufbau Principle: Electrons populate orbitals from lower to higher energy.

  

• Pauli Exclusion Principle: A maximum of two electrons can reside in each orbital, maintaining opposite spins.

• Hund's Rule: Electrons occupy equal-energy orbitals singly before pairing up.

Worked Example: Electron Configuration

For the element calcium (Ca, atomic number 20):

1. Identify the total number of electrons: 20
2. Follow the Aufbau filling order: 1s → 2s → 2p → 3s → 3p → 4s
3. Fill each orbital according to capacity:
   • 1s: 2 electrons
   • 2s: 2 electrons
   • 2p: 6 electrons
   • 3s: 2 electrons
   • 3p: 6 electrons
   • 4s: 2 electrons
4. Therefore, the electron configuration is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s²

Periodicity and Trends

• Influence on Properties:

  • Ionisation Energy & Electronegativity: Tend to increase across a period.
  • Atomic Radius: Typically decreases across a period.

  

Practice Question with Solution

Question: Determine the four quantum numbers for the last electron in a nitrogen atom (atomic number 7).

Solution:

1. Electron configuration of nitrogen: 1s² 2s² 2p³
2. The last electron is in a 2p orbital
3. Principal quantum number (n) = 2
4. Azimuthal quantum number (l) = 1 (p orbital)
5. Magnetic quantum number ($m_l$) = -1, 0, or +1 (since p orbitals have these orientations)
6. According to Hund's rule, the p orbitals will each have one electron first, so the last electron is in the third p orbital with $m_l$ = +1
7. Spin quantum number ($m_s$) = +½ (assuming first electron in each orbital has spin up)
8. Therefore, the quantum numbers are: n = 2, l = 1, $m_l$ = +1, $m_s$ = +½

Special Notes on Exceptions

Understanding these configurations is crucial for interpreting chemical reactivity and periodic trends.