Gen Chem 1.1 to 1.2

• Atomic structure and the birth of quantum mechanics are covered.
• The topics include the nature of light, atomic spectroscopy and the Bohr model, the wave nature of matter, and quantum mechanics and the atom.

A History of the Atom: Theories and Models

• This graphic looks at atomic models and how they developed.
• In 1803, John Dalton drew upon the Ancient Greek idea of atoms and his theory stated that atoms are indivisible, those of a given element are identical, and compounds are combinations of different types of atoms.
• In 1904, J.J. Thomson discovered electrons in atoms in 1897, for which he won a Nobel Prize, produced the 'plum pudding' model which shows the atom as composed of electrons scattered throughout a spherical cloud of positive charge.
• In 1911, Ernest Rutherford fired positively charged alpha particles at a thin sheet of gold foil, and realized positive charge was localized in the nucleus of an atom.
• In 1913, Niels Bohr modified Rutherford's model of the atom by stating that electrons moved around the nucleus in orbits of fixed sizes and energies with electron energy was quantised.
• In 1926, Erwin Schrödinger stated that electrons do not move in set paths around the nucleus, but in waves and it is impossible to know the exact location of the electrons.

The Electronic Structure of Atoms

• Continuous vs. (atomic) line emission spectra are discussed.
• In 1913, Niels Bohr proposed that electrons do NOT whirl around the nucleus like a solar system, but instead can only occupy certain “orbits” of specific energies.
• The energy of electrons is quantized, and atoms and molecules have only certain allowable, discrete energy levels.
• Unique for each atom / ion / molecule / system.

The Bohr Model

• "n" represent an “orbit”, or “energy level".
• n=1 is the ground state.
• n>1 is the excited state.
• As "n" increases distance from the nucleus increases as n increases and energy levels get closer and closer in proximity (exponential function).
• For an electron in the Hydrogen atom: En = the energy of an electron in orbit "n" (J).
• R = 3.29 x 10^15 s^-1.
• h = Planck's constant = 6.626 x 10^-34 J*s.
• Bohr attributed the emission of radiation by an energized hydrogen atom to an electron transitioning from a higher energy orbit to a lower energy orbit, emitting a "quantum" (photon) of energy in the form of light.

Importance and Limitations of the Bohr Model

• The importance of the Bohr model is that it introduced the concept that electrons exist in energy levels.
• As electrons transition between levels, energy is exchanged.
• Limitations of the Bohr model are that it describes electrons in specific orbits, like books on a shelf, in an exact position and explains the Hydrogen atom EXACTLY, but is applicable for only one electron systems.
• De Broglie asserted that a moving particle (such as an electron) also has wave-like properties.
• Quantum mechanics is a more comprehensive way to understand the structure of the atom, which accounts for wave-particle duality, the quantization of energy, and the Heisenberg Uncertainty Principle.
• Heisenberg uncertainty principle: it is impossible to simultaneously know both the position and momentum of an electron.

Quantum Mechanics and the Schrödinger Equation

• In 1926, Erwin Schrodinger formulated an equation that describes the location and behavior of an electron in an atom.
• Incorporates both particle behavior (mass) and wave behavior (wavefunctions, ψ).
• Electron wavefunction in radial coordinates ψ(r,θ,φ) can be separated into a radial and an angular part.
• Energy states and wave functions (ψ) of an electron are characterized by a set of quantum numbers.
• Four quantum numbers describe the distribution and behavior of electrons in an atom.
• 1. Principal quantum number (n).
• 2. Angular momentum quantum number (1)→ distribution] "Orbital".
• 3. Magnetic quantum number (mℓ).
• 4. Magnetic spin quantum number (Ms).

Quantum Numbers: Atomic Orbitals, Nodes, and Radial Distribution Plots

• Quantum mechanics and the atom, and the shapes of atomic orbitals are included in discussions on quantum numbers, atomic orbitals, nodes, and radial distribution plots.
• The website for visualizing atomic orbitals, nodes, and radial distribution plots is https://winter.group.shef.ac.uk/orbitron/atomic_orbitals/3d/index.html.

Quantum Numbers

• Principal quantum number (n) designates the size and energy and is referred to as energy level or shell.
• Higher n value = larger shell = further from nucleus, with allowed integer values.
• Angular momentum quantum number (ℓ), or subshell, primarily designates the shape of an orbital.
• Allowed values depend on n can be n=0 to n=-1 with numbers corresponding to letter designations: 0 → s, 1 → p, 2 → d, 3 → f.

Quantum Numbers

• Magnetic quantum number (m₁) is referred to as orbital, and primarily designates the orientation in space (x, y, z).
• Allowed values depend on l and can be -l... 0...+l.
• The wave function of an electron in an atom is a depiction of the physical region around the nucleus that encloses 90% of the total electron probability.
• Magnetic spin quantum number (ms) describes the spin of an electron within an orbital and only two possible values + 1/2 or -1/2 (spin up or spin down).
• The maximum number of electrons per orbital = 2.

Nodes

• A node is a point in which the probability of finding electron density in an atom is zero.
• The position on a standing wave where the amplitude is zero.
• The total number of nodes for an orbital = n-1.
• Two types: planar (angular) and radial.
• Planar (angular) nodes (nodes that are planar) are dictated by orbital shape and the # of planar nodes = ℓ.
• Radial nodes (spherical) are dictated by shape (l) and size (n), and the # radial nodes = n-l-1.

s-orbitals

• As n increases, the number of nodes increases.

p-orbitals

• px, py, and pz orbitals are shown.

d-orbitals

• There is electron density on these axes/between ones on that plane.

Chemistry Across the Periodic Table

• The chemistry of Main Group elements depends strongly on the s, p-orbitals.
• The chemistry of Transition Metals elements depends strongly on the d-orbitals.

Quantum Numbers

• Summary of allowable combinations of quantum numbers are provided.

Quantum Numbers

• There are several practice questions related to providing a plausible set of 4 quantum numbers for an electron in each orbital. The questions are:
  • How many orbitals are there in the subshell designated ℓ = 2?
  • How many electrons can be contained in a 4d subshell?
  • Provide a plausible name for an atomic orbital with the following set of quantum numbers: n = 4, I = 1, mℓ = -1, m₃ = + ½.

Graphical Interpretation of Wavefunctions

• (1) ψ = wavefunctions are solutions of the Schrodinger equation.
• Crossing x-axis indicates a change in phase or amplitude.
• (2) ψ² = probability density; the probability of finding an electron near distance (r), at location (x, y, z)
• Amplitude is always positive.
• Radial wavefunctions for 1s, 2s, and 3s orbitals are provided.

Radial Probability Distribution Functions

• (3) Ψ²r² = radial probability distribution function: Probability of finding an electron at a given radius, summed over all directions (x,y,z) of an atom (accounting for volume). The number of times the curve touches the x-axis = # of radial nodes.
• As n increases, the probability of finding an electron further away from the nucleus increases.
• It's probable to find an electron near the nucleus but not in the nucleus.

Practice

• Practice exam-like questions are provided given radial distribution plots and orbital shape, and what the orbital name is.
• The bonus question is to provide a plausible set of 4 quantum numbers for an electron in each orbital.

Explore the fundamental concepts of quantum mechanics. Questions cover wave-particle duality, the Schrödinger equation, the Heisenberg Uncertainty Principle, and the Bohr model. Test your knowledge of quantum mechanics.