Lecture 5: Electrons and Bonding

Electrons and Bonding

Covalent Chemical Bonds

Covalent chemical bonds typically consist of 1, 2, or 3 pairs of electrons shared between atoms, forming single, double, and triple bonds respectively.

Chemical Reactions

Chemical reactions generally involve the reorganization of electrons in bond-making and bond-breaking processes.

Redox Reactions

Redox reactions involve the transfer of one or more electrons between chemical species. This transfer can lead to ionic bonding if cations and anions are formed.

Importance of Electrons

The chemical properties of an element and its reactivity are primarily determined by its electrons.

Electromagnetic Spectrum

Electromagnetic radiation is described as waves characterized by wavelength (\lambda) and frequency (\nu).

• Wavelength (\lambda): The distance between two adjacent identical points in a wave.
• Frequency (\nu): The number of wave crests passing a given point per unit time, measured in s⁻¹ or cycles per second (Hz).
• Relationship: \lambda \nu = c, where c is the speed of light (3 \times 10^8 m/s).

Light as Waves

Visible light exhibits wave properties, including wavelength (\lambda in nm) and frequency (\nu in s⁻¹ = Hz).

• Diffraction: Light diffracts readily, as seen in the classic 2-slit experiment.
• Interference: Interference fringes are created, forming an interference pattern.
• In-phase waves: Add together to produce bright spots.

Light as Particles

Visible light also exhibits particle properties:

• Photoelectric Effect: When light is shone on certain metals (e.g., zinc), photoelectrons are emitted.
• Threshold Frequency: Each metal has a minimum frequency of light below which no photoelectrons are emitted.
• Einstein's Contribution: Einstein established that E = h\nu, where a specific frequency (\nu) of light is required to release photoelectrons; h is Planck’s constant.
• Photons: This confirmed that light is composed of particles called photons.
• Wave/Particle Duality: Light exhibits both wave and particle properties.

Wave/Particle Duality of Electrons

Electrons exhibit both particle and wave properties.

• Cathode Ray Tube: In a cathode ray tube, an electron beam is guided by charged plates, demonstrating the particle nature of electrons.
• Electron Diffraction: A beam of electrons directed at a sample produces interference patterns, which can be used to determine the structure of the sample, demonstrating the wave nature of electrons.

The Bohr Atom

The Bohr model describes atomic structure with electrons in specific spherical orbits around the nucleus.

• Model Description: The nucleus contains protons and neutrons, surrounded by electrons in their own spherical orbits.
• Hydrogen Atom: Bohr primarily worked on the hydrogen atom.
• Energy Levels: Each atomic state corresponds to the electron being in a specific energy level, at a certain distance from the nucleus.

Absorption Spectra

Light can be used to investigate the electronic structure of atoms.

• Atomic Spectra: Atoms absorb or emit specific frequencies of light.
• Measurement: The absorption spectrum of a gaseous element can be readily measured.
• Process: Light is absorbed by the atom, causing an electron to move from the lowest orbit (ground state) to a higher orbit (excited state).
• Ground State: The lowest energy state of an atom.
• Excited State: A higher energy state than the ground state.

Emission Spectra

• Measurement: The emission spectrum of a gaseous element can also be measured.
• Process: Light is emitted when an atom in a high-energy situation releases a photon as an electron relaxes from a higher energy orbit back to the lowest energy orbit.
• Information: The characteristic patterns of energy gains and losses provide information about atomic structure.

Atomic Spectra (H2)

In the emission spectrum of H2, the H2 molecule is dissociated into H atoms and electronically excited by an electric discharge.

• Process: Electrons are excited into high energy orbitals and then drop back to low energy orbitals, releasing energy.
• Transitions: Each transition corresponds to a line seen in the emission spectrum (e.g., n=3 \rightarrow n=2 in the visible series).

Atomic Emission Spectra

In the Bohr atom, emission can be explained by the expression:

• E{photon} = h\nu{photon}
• \Delta E = E{atom-highEstate} - E{atom-lowEstate}
• \Delta E = \frac{hc}{\lambda_{photon}}, where \lambda is wavelength in nm, c is the speed of light (3.00 \times 10^8 ms⁻¹), and h is Planck’s constant (6.63 \times 10^{-34} J.s).
• Lowest Energy State: Ground state (electron(s) closest to the nucleus).
• Next Highest Energy State: 1st Excited state.

Energy Level Diagrams

Atomic energy transformations can be represented using an energy level diagram.

The Quantised Electron

The energy change for atomic states equals the energy change for an atomic electron:

• \Delta E{atom} = \Delta E{electron} = h\nu
• Quantisation: A property restricted to specific values is said to be quantised.
• Implication: The changes in electron energy indicate that electrons behave in a quantized fashion.

The Quantum Mechanical Atom

• Limitation of Bohr’s Model: Bohr’s model fails for multi-electron atoms.
• Quantum Mechanics: A physical model governing electron motion, allowing atomic energies to have only discrete values (quantised).
• Schrödinger Equation: \hat{H} \Psi = E \Psi, where \Psi is the atomic wavefunction, E is atomic energy, and \hat{H} is the Hamiltonian operator.
• Orbitals: Solutions to the Schrödinger equation are possible one-electron wavefunctions also called atomic orbitals.
• Uncertainty Principle: We can only describe the probability of finding an electron at a particular position about the nucleus.

Electron Probability Distributions

• \Psi^2: Electron probability distribution (\Psi^2 at a point in space).
• Measurable: Although \Psi is not experimentally observable, the function \Psi^2 is measurable.

Atomic Orbitals

• Definition: A region in space about a nucleus where there is a high probability of finding an electron.
• s-orbital: The ground state inner-most orbital (1s) is spherically symmetric.
• Higher Energy Orbitals: May have s-orbital shape or more complex p-orbital or d-orbital shapes.
• Orientation: The p- and d-orbitals have fixed orientations with respect to the x, y, z axes (e.g., px, py, dz²).

Quantum Numbers

The 1-electron atomic wavefunction \Psi, also called an atomic orbital, is specified by three quantum numbers: n, l, ml (e.g., 2px: n=2, l=1, ml = -1).

• Principal Quantum Number (n): n = 1 … N, defines the shell.
• Angular Quantum Number (l): l = 0 … n-1, defines the subshell (l = 0 = s, l = 1 = p, l = 2 = d).
• Magnetic Quantum Number (ml): m_l = -l … 0 … +l, defines the orientation.

Atomic Orbitals - Orbital Size

• Size: Orbitals increase in size as the value of n increases.
• Similarity: All orbitals with the same principal quantum number n are similar in size.
• Multi-electron Atoms: An atom with many electrons can be described by superimposing the orbitals.

Quantum Numbers - n

• Identification: Each quantised property is identified using a quantum number.
• Spatial Properties: An electron has three quantum numbers specifying spatial properties (n, l, m_l).
• Spin: A fourth number describes electron spin (m_s).
• Principal Quantum Number (n):
  • Correlated with orbital size.
  • Must be a positive integer (1, 2, …).
  • As n increases, the energy increases, the orbital gets bigger, and electrons are less tightly bound.

Quantum Numbers – l, ml

• Angular Quantum Number (l):
  • Identifies the shape of the electron distribution (sub-shell).
  • Can be zero or any positive integer smaller than n (i.e., l = 0, 1, …, n-1).
  • Indexes the angular momentum of the orbital.
  • l = 0 (s), l = 1 (p), l = 2 (d), l = 3 (f).
• Magnetic Quantum Number (m_l):
  • Indexes the restricted number of possible orientations of the sub-shells.
  • Can have values between -l and +l.

Quantum Numbers - ms

• Spin Quantum Number (m_s):
  • Electrons have a property called spin.
  • Can behave in one of two ways in a magnetic field.
  • Indexes behaviour in a magnetic field.
  • Can have values of -\frac{1}{2} and +\frac{1}{2}.
• Specification: An electron in an orbital is specified by the 4 quantum numbers: n, l, ml, ms.

Specifying an Atomic Orbital

The principal quantum number n indicates how far out from the nucleus the peak in electron density is.

• Angular Quantum Number Rule: l = 0 … n-1.
• Example: For n = 3, l = 2, 1, 0, indicating s (l=0), p (l=1) and d (l=2) orbitals are available.
• Magnetic Quantum Number Rule: m_l = -l … 0 … +l.
• Example: For l = 1, m_l = -1, 0, +1, indicating px, py, pz orbitals are available.

Pauli and Hunds Rules

• Spin Quantum Number: m_s = +\frac{1}{2} or -\frac{1}{2} (spin up  or spin down ).
• Pauli Exclusion Principle: No 2 electrons in the same atom can have the same 4 quantum numbers.
• Hund’s Rule: The lowest energy configuration involving orbitals of equal energies (degenerate) is the one with the maximum number of electrons of the same spin.

s and p Orbitals

• Interactions: Electron interactions can be described in terms of orbital interactions.
• s orbitals: l = 0 corresponds to an s orbital. There is only one s orbital for each value of the principal quantum number n (e.g., 1s, 2s).
• p orbitals: l = 1 corresponds to a p orbital. For each value of n > 1, there are three different p orbitals (m_l = -1, 0, +1) (e.g., 2px, 3px).

d Orbitals

• d orbitals: l = 2 corresponds to a d orbital. There are five different d orbitals (m_l = -2, -1, 0, +1, +2).
• Existence: d orbitals only exist when n \geq 3 (e.g., 3dz², 4dz²).