CHM1011 week 2 lecture slides

Week 2 Online Lecture 1: Orbitals

Weekly Objectives

• Recognise the dual nature of light and inter-relationship of its properties.

• Understand the relationship between wave function and orbitals.

• Distinguish quantum numbers.

• Explain the general features of atomic orbitals and draw different representations.

• Recognise ‘nodes’ – planar and radial – as important features of orbitals.

• Examine the relationship between quantum numbers, electron penetration, and shielding.

Orbitals

• The representation of an atom is found to be inaccurate.

• Electrons do not follow circular orbits.

• Schrödinger equation:

  • Electrons exhibit both wave-like and particle-like behavior.

  • Probability of finding an electron at certain points in space around the nucleus.

Probability Density

• Describes the likelihood of locating an electron at a specific point in space, denoted by Ψ², regarding the distance (r) from the nucleus.

Radial Density Function

• Defines the probability of finding an electron within a spherical shell at a distance 'r' from the nucleus.

• As 'r' increases, the volume of shells increases, affecting the radial density function.

• This function shows a rise to a maximum before decreasing back to zero.

Atomic Orbitals

• Defined as the solutions to the Schrödinger equation, representing the energy level for electrons.

• Described mathematically rather than as a distinct region in space.

• Probability of finding an electron decreases with increasing distance from the nucleus.

• Each orbital has a unique shape linked to the likelihood of finding an electron 95% of the time across x, y, and z axes.

Quantum Numbers

• Represent unique solutions to Schrödinger's equation, where each electron has its own set of four quantum numbers:

  • Principal (n): Positive integers (1, 2, 3, ...), defining orbital energy (shells).

  • Angular Momentum (l): Integers from 0 to n-1, defining shape.

  • Magnetic (ml): Integers from -l, 0, +l, defining orientation.

  • Spin (ms): Values of -1/2 or +1/2, indicating electron spin.

Angular Momentum Quantum Number (l)

• Labels for values of l:

  • l = 0: orbital = s

  • l = 1: orbital = p

  • l = 2: orbital = d

  • l = 3: orbital = f

• Example: For n = 3 and l = 2, indicates a 3d orbital.

Orbital Energies

• Increased n and l values lead to increased energy in orbitals.

• Electrons occupy orbitals starting from the lowest energy upwards.

• Remembering orbital filling order:

  • n values remain constant horizontally.

  • l values remain constant vertically.

  • Combined (n + l) values are consistent diagonally.

Quantum Number Trivia Activity

1. Determine principal and angular quantum numbers for a 3d orbital.

2. Calculate available angular momentum quantum numbers with principal quantum number 1.

3. For n=2, determine total magnetic quantum number solutions.

4. Determine possible angular momentum quantum numbers for principal quantum number 3.

5. Identify possible quantum numbers for an electron in a 2s orbital.

Summary

• Dispelled the notion of circular electron orbits.

• Analyzed electron probabilities in atoms.

• Catalogued energy ranges of atomic orbitals through quantum numbers.

• Explained the correlation between atomic orbital energies and their electron filling order.

Week 2 Online Lecture 2: Orbitals

s Subshell Orbitals

• Contains one orbital and can hold a maximum of 2 electrons.

• Exhibits a spherical shape.

p Subshell Orbitals

• Encompasses three orbitals: px, py, pz.

• Maximum capacity is 6 electrons.

• Characterized by a ‘dumbbell’ shape.

d Subshell Orbitals

• Comprises five orbitals: dxy, dyz, dxz, dx²-y², dz².

• Holds a maximum of 10 electrons.

• Demonstrates a ‘double-dumbbell’ shape.

Nodes

• Nodal Plane: A plane in space where the wavefunction shows zero probability amplitude.

• The number of planar nodes equals l.

  • 2p-orbitals contain one nodal plane.

  • 3d-orbitals have two nodal planes.

Radial Nodes

• Locations in orbitals where the wavefunction has zero probability amplitude for finding electrons.

• Total nodes formula: n - 1.

Activity 1

1. Identify quantum numbers for various atomic orbitals and discuss the presence of nodes:

   • a) 2p

   • b) 3d

   • c) 2s

2. Identify atomic orbitals given quantum numbers and use radial distribution graphs for determining node counts:

   • a) n=1, l=0, ml=0

   • b) n=3, l=1, ml=0

   • c) n=3, l=2, ml=-1.

Penetration and Shielding

• Compare electron density at different n levels.

• Note: 3s has two radial nodes, 3p has one, and 3d has none.

Stability Through Penetration

• The 2s orbital penetrates closer to the nucleus than the 2p orbital, shielding it and thus making the 2s orbital lower in energy and more stable.

• Electrons in the 3p orbital also shield 3d orbitals, giving the order of energy: 3s < 3p < 3d.

Summary

• Investigated shapes for s, p, and d atomic orbitals.

• Explored types of nodes in atomic orbitals.

• Compared stability and energy between atomic orbitals regarding penetration and shielding.

Copyright Notice

• This material is reproduced under the Copyright Act 1968. Further reproduction or communication may be subject to copyright.