CHEM Topic 3d lecture

Quantum Mechanical Model of Electrons

• The current model for describing electrons is the quantum model or wave mechanical model.
• Electrons exist in specific clouds or orbitals around atoms.
• These orbitals are subsets within energy levels.

Quantum Numbers: Electron Addresses

• Quantum numbers provide an "address" for each electron around an atom.
• These numbers indicate the most probable location and orientation of electrons.
• Due to the uncertainty principle, we cannot definitively know the exact location of an electron; the act of observing it alters its position. This is also related to Heisenberg's Uncertainty Principle.
• No two electrons can have the same set of quantum numbers; each electron has a unique address in space and time.

Nucleons: Protons and Neutrons

• The nucleus contains protons and neutrons, collectively referred to as nucleons.
• Protons:
  • Have a positive charge (+1 atomic charge).
  • Have a mass of 1 AMU (atomic mass unit).
  • $1 \text{ AMU} \approx 1 \text{ gram per mole}$
• Neutrons:
  • Have no charge (0 charge).
  • Have a mass of 1 AMU.

Four Quantum Numbers: Detailed Breakdown

• These numbers act like components of an address: house number, street, city, and state.
• Principal Quantum Number (n):
  • Symbol: $n$
  • Represents the energy level of an electron. This is the main energy level or shell the electron occupies.
• Secondary Quantum Number (l):
  • Symbol: $l$
  • Indicates the sublevel or shape of the electron's orbital (s, p, d, f).
• Magnetic Quantum Number ($m_l$ or m):
  • Symbol: $m_l$
  • Specifies the orbital within a sublevel that the electron occupies. This relates to the spatial orientation of the orbital.
• Spin Quantum Number ($m_s$ or s):
  • Symbol: $m_s$
  • Describes the spin orientation of the electron (+1/2 or -1/2).

Principal Energy Levels (n)

• Electrons in higher energy levels have more potential energy, similar to an object's potential energy increasing with height above the Earth.
• Valence Electrons:
  • Located in the outermost energy level (valence shell).
  • Primarily involved in chemical reactions, including sharing, gaining, or losing electrons.

Electron Excitation and Emission

• Ground State: The lowest possible energy level an electron can occupy; the default state.
• Excitation: Electrons absorb energy from the environment (e.g., light, heat) and jump to higher energy levels.
  • Absorption of light energy: Shining light on an atom can excite electrons.
  • Heating: Increased heat can excite electrons, leading to phenomena like glowing or fire.
• Emission: When excited electrons return to their ground state, they release energy in the form of light (photons).
  • The light emitted corresponds to the energy difference between the excited state and the ground state.

Absorption and Emission Spectra

• Absorption Spectrum: The specific wavelengths of light that an element absorbs when its electrons get excited.
  • Shining white light (containing all colors) through a gas results in the gas absorbing certain wavelengths, seen as black lines in the spectrum.
• Emission Spectrum: The specific wavelengths of light that an element emits when its electrons return to the ground state.
  • These wavelengths correspond to the colors emitted by the element.
• Bohr's Contribution: Bohr used emission and absorption spectra to determine the existence of energy levels in atoms.
• Wavelength and Energy:
  • Violet light has shorter wavelengths and higher energy than red light.
  • Ultraviolet (UV) light, beyond violet, is high-energy and can damage DNA, leading to cancer and skin burns.
  • Infrared (IR) light, just below red, is lower in energy, but can still cause heating due to the large number of photons emitted.

Hydrogen Emission: Example

• Visible light emitted by excited hydrogen results from electrons transitioning from higher energy levels to the second energy level.
• Infrared light is emitted when electrons transition to the third energy level, though it is not visible.
• UV lamps with hydrogen excite the gas, causing electrons to fall to the first energy level and emit ultraviolet light.

Capacity of Energy Levels

• Each energy level can hold a specific number of electrons, determined by the formula:$\text{Number of electrons} = 2n^2$
  • n = 1 (first energy level): $2(1)^2 = 2$
  • n = 2 (second energy level): $2(2)^2 = 8$
  • n = 3 (third energy level): $2(3)^2 = 18$
  • n = 4 (fourth energy level): $2(4)^2 = 32$
• Current understanding suggests that energy levels beyond the fourth likely hold a maximum of 32 electrons, based on graduate-level nuclear physics and chemistry research.

Sublevels or Orbital Shapes (l)

• Each energy level contains one or more sublevels, designated as s, p, d, and f.
  • First energy level: only s sublevel.
  • Second energy level: s and p sublevels.
  • Third energy level: s, p, and d sublevels.
  • Fourth energy level and higher: s, p, d, and f sublevels.
• Each sublevel can hold a specific number of electrons:
  • s: 2 electrons
  • p: 6 electrons
  • d: 10 electrons
  • f: 14 electrons

Filling of Electrons and Overlapping

• Ideally, sublevels would fill in order of increasing energy (1s, 2s, 2p, 3s, 3p, etc.).
• However, there is some overlap in energy levels between sublevels from one energy level to the next.
• Example: The 4s sublevel has slightly lower energy than the 3d sublevel, so it fills first.
• This overlapping begins at the fourth energy level and becomes more complex at higher levels.

Orbitals (m_l/m): Spatial Orientation

• Orbitals, also known as clouds, describe the spatial orientation of sublevels.
• The number of orbitals per sublevel:
  • s sublevel: 1 orbital
  • p sublevel: 3 orbitals
  • d sublevel: 5 orbitals
  • f sublevel: 7 orbitals
• Each orbital can hold a maximum of two electrons.
  • This explains why the s sublevel holds 2 electrons (1 orbital x 2 electrons), the p holds 6 (3 orbitals x 2 electrons), the d holds 10 (5 orbitals x 2 electrons) and the f hods 14 (7 orbitals x 2 electrons).

Organization of the Periodic Table

• The periodic table is organized based on how electrons fill energy levels and sublevels.
• Columns (groups) indicate the number of valence electrons.
• The first two columns (groups 1 and 2) represent the filling of the s sublevel, which holds two electrons, thus the two columns.
• Groups 13-18 (skipping the transition metals) represent the filling of the p sublevel, which holds six electrons, corresponding to the six columns.
• The transition metals represent the filling of the d sublevel, with 10 columns for the 10 electrons.
• The lanthanide and actinide series (usually shown separately) represent the filling of the f sublevel, with 14 columns.

Orbital Shapes

• The shape of an orbital depends on its sublevel.
  • s orbitals: spherical.
  • p orbitals: dumbbell-shaped, with three different orientations along the x, y, and z axes.
  • d and f orbitals: more complex shapes.

Spin Quantum Number (m_s) and Electron Pairing

• The spin quantum number describes the electrical orientation of an electron.
• Two electrons occupying the same orbital must have opposite spins (+1/2 and -1/2).

Summary of Quantum Numbers

• Each electron has a unique set of quantum numbers:
  • n: energy level
  • l: sublevel
  • $m_l$: orbital
  • $m_s$: spin
• These four numbers create a unique "serial number" or address for each electron in an atom.