CHEM 6A: Atomic Structure, Quantum Theory, and Chemical Bonding

A comprehensive vocabulary review of atomic structure, early atomic physics, quantum theory, hydrogen wavefunctions, multi-electron atoms, periodic trends, ionic and covalent bonding, Lewis formal charges, and VSEPR molecular geometry.

Nuclear Model of the Atom

The atomic model established by Ernest Rutherford (1910) where all positive charge (protons) and nearly all mass (protons and neutrons) are concentrated in a tiny central nucleus, surrounded by low-mass, negatively charged electrons occupying a relatively large volume.

Plum Pudding Model

The atomic model proposed by J.J. Thomson following his discovery of the electron in 1897, envisioning the atom's positive charge diffusely spread like jelly over a region with negatively charged electrons suspended within it like raisins.

Alpha (\alpha) Particle

A positively charged particle consisting of two protons and two neutrons, making it identical to the nucleus of a helium-4 atom ($^4\text{He}$).

Millikan's Oil-Drop Experiment

A 1909 experiment conducted by Robert Millikan that determined the fundamental charge of an electron ($-1.602 \times 10^{-19}\,\text{C}$), which in conjunction with J.J. Thomson's charge-to-mass ratio ($-5.686 \times 10^{-12}\,\text{kg}\,\text{C}^{-1}$) determined the electron mass to be $9.109 \times 10^{-31}\,\text{kg}$.

Electromagnetic Radiation

A form of energy consisting of oscillating electric and magnetic fields traveling as sine waves at right angles to one another at the speed of light in a vacuum ($c = 3.00 \times 10^8\,\text{m/s}$).

Wavelength (\lambda)

The peak-to-peak distance of an electromagnetic wave, typically measured in meters ($\text{m}$) or nanometers ($\text{nm}$, where $1\,\text{nm} = 10^{-9}\,\text{m}$).

Frequency (\nu)

The number of complete wave cycles that pass a given point per second, expressed in Hertz ($\text{Hz}$ or $\text{s}^{-1}$), related to wavelength and wave speed by $c = \lambda\nu$.

Lyman Series

The group of spectral emission lines for atomic hydrogen occurring in the ultraviolet region of the electromagnetic spectrum, resulting from electronic transitions terminating at $n_1 = 1$.

Balmer Series

The group of spectral emission lines for atomic hydrogen occurring in the visible light spectrum, corresponding to electronic transitions terminating at $n_1 = 2$.

Rydberg Constant (R)

The empirical constant used to calculate the frequencies of spectral lines in hydrogen, defined as $R = 3.29 \times 10^{15}\,\text{Hz}$ in the formula $\nu = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$, where $n_1 < n_2$.

Bohr Atomic Theory

A model of the hydrogen atom proposed by Niels Bohr where an electron can occupy only discrete, allowed energy levels ($E_n = -\frac{R_H}{n^2}$, with $R_H = 2.18 \times 10^{-18}\,\text{J}$), emitting or absorbing radiation matching $\Delta E = h\nu$ when transitioning between states.

Blackbody

An idealized physical body that absorbs and emits radiation of all wavelengths equally well.

Ultraviolet Catastrophe

The failure of classical mechanics (the Rayleigh-Jeans Law) to predict blackbody radiation, incorrectly asserting that the radiated energy density should increase toward infinity as frequency rises.

Planck's Quantum Hypothesis

The postulate formulated by Max Planck stating that atoms absorb and emit energy only in discrete packets called quanta, whose energy is quantized in whole-number multiples of $h\nu$ ($E = nh\nu$, where $h = 6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$).

Photoelectric Effect

The ejection of electrons from a metal surface when irradiated with light of frequency higher than a specific threshold ($\nu > \nu_0$), demonstrating the particle-like nature of light.

Work Function (\Phi)

The characteristic minimum threshold energy required to eject an electron from the surface of a given metal, defined by $\Phi = h\nu_0$.

Photon

A spatially localized packet of light energy that behaves as an elementary particle with energy directly proportional to its frequency: $E_{\text{photon}} = h\nu = \frac{hc}{\lambda}$.

Constructive Interference

The wave phenomenon that occurs when the peaks of two in-phase waves coincide, combining their amplitudes to form a wave of greater net amplitude.

Destructive Interference

The wave phenomenon that occurs when the peaks of one wave coincide with the troughs of an out-of-phase wave, diminishing or canceling the resulting net amplitude.

Diffraction

The bending and spreading of waves around obstacles or through slits whose dimensions are comparable to the wavelength of the waves, producing an interference pattern.

de Broglie Wavelength

The wavelength associated with any moving matter, calculated via $\lambda = \frac{h}{mv} = \frac{h}{p}$, demonstrating the wave-particle duality of matter.

Heisenberg Uncertainty Principle

The fundamental quantum principle stating that it is impossible to simultaneously measure both the precise position ($\Delta x$) and linear momentum ($\Delta p$) of a particle: $\Delta p \Delta x \ge \frac{1}{2}\hbar$, where $\hbar = \frac{h}{2\pi}$.

Wavefunction (\psi)

A mathematical function derived from the Schrödinger equation that varies with position and contains all knowable physical information regarding a quantum mechanical system.

Probability Density

The physical property represented by $\psi^2$ (or $|\psi|^2$), indicating the probability per unit volume of finding a particle at a specific coordinate in space.

Node

A point, plane, or surface where a wavefunction passes through zero ($\psi = 0$), denoting a location where the probability density of finding the particle is zero.

Zero-Point Energy (ZPE)

The lowest possible non-zero energy state that a quantum system (such as a particle in a box) can possess ($n = 1$), preventing a quantum particle from ever being completely stationary.

Principal Quantum Number (n)

The quantum number ($n = 1, 2, 3, \dots$) that specifies the main electronic energy level (shell) and primarily dictates the size and energy of an orbital.

Orbital Angular Momentum Quantum Number (l)

The quantum number that designates orbital shape and subshell identity, taking integer values from $0$ to $n - 1$ ($l = 0, 1, 2, 3$ corresponding to $s, p, d, f$ subshells).

Magnetic Quantum Number (m_l)

The quantum number that describes the spatial orientation of an orbital within a given subshell, taking integer values ranging from $-l$ to $+l$ ($2l + 1$ allowed orientations).

Spin Quantum Number (m_s)

The fourth quantum number describing the intrinsic angular momentum of an electron, which can take values of either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Degenerate Orbitals

Orbitals that possess precisely the same energy level (such as all orbitals in a given shell $n$ for atomic hydrogen, or subshell orbitals in multi-electron atoms).

Radial Distribution Function

A mathematical function ($4\pi r^2 \psi^2$) that gives the total probability of finding an electron within a thin spherical shell at distance $r$ from the nucleus, summed across all angular directions.

Nodal Plane

A flat plane passing through the nucleus where the electron wavefunction passes through zero ($\psi = 0$), resulting in zero probability of finding an electron (e.g., the plane separating the two lobes of a $p$-orbital).

Effective Nuclear Charge (Z_{eff})

The net positive nuclear charge experienced by a valence electron, which is smaller than the actual nuclear charge $Z$ due to repulsive shielding interactions by other electrons ($Z_{\text{eff}} < Z$).

Shielding

The repulsive electrostatic force exerted by inner-shell (core) electrons on outer electrons that partially counteracts the attractive pull of the nuclear charge.

Orbital Penetration

The ability of an electron in an orbital with lower $l$ (such as $s$) to spend a portion of its time very close to the nucleus due to an inner radial probability maximum, reducing the shielding it experiences and lowering its energy relative to other subshells in the same shell ($ns < np < nd < nf$).

Aufbau Principle

The guideline stating that in the ground state of an atom, electrons occupy the lowest-energy available orbitals first before moving into higher-energy states.

Pauli Exclusion Principle

The quantum rule established by Wolfgang Pauli stating that no two electrons in an atom can possess the identical set of four quantum numbers ($n, l, m_l, m_s$), restricting any single orbital to a maximum of two electrons with opposing spins.

Hund's Rule

The rule formulated by Friedrich Hund stating that for degenerate orbitals, the lowest-energy electron configuration maximizes the number of unpaired electrons with parallel spins before pairing starts.

Core Electrons

Inner electrons residing in filled shells corresponding to the previous noble gas electron configuration that do not participate in chemical bonding.

Valence Electrons

Electrons residing in the outermost unfilled shell (highest principal quantum number $n$) of an atom that are directly involved in forming chemical bonds.

Atomic Radius

Half the distance between the nuclei of neighboring atoms in a metallic solid or a homonuclear diatomic molecule, which generally increases down a group and decreases across a period.

Isoelectronic Species

Atoms and ions that share the identical total number of electrons and identical ground-state electron configurations (such as $\text{Mg}^{2+}$, $\text{Na}^+$, and $\text{F}^-$).

First Ionization Energy (I_1)

The minimum energy required to remove the most loosely held electron from a neutral, gaseous atom in its ground state: $X(g) + I_1 \rightarrow X^+(g) + e^-$.

Second Ionization Energy (I_2)

The minimum energy required to remove an electron from a singly charged gas-phase cation: $X^+(g) + I_2 \rightarrow X^{2+}(g) + e^-$.

Electron Affinity (E_{ea})

The energy change or release associated with adding an electron to an isolated gas-phase atom: $X(g) + e^- \rightarrow X^-(g) + E_{\text{ea}}$.

Ionic Bond

A chemical bond formed via the complete transfer of one or more valence electrons from a metal atom to a nonmetal atom, resulting in cations and anions held together by electrostatic attraction in a crystal lattice.

Covalent Bond

A chemical bond formed when two nonmetal atoms achieve lower potential energy by sharing one or more pairs of valence electrons.

Metallic Bond

A type of chemical bonding characteristic of metals where an array of fixed metal cations is held together by delocalized valence electrons pooled into a mobile electron sea.

Lattice Energy

The energy released when separated gas-phase ions coalesce to assemble one mole of an ionic solid crystalline lattice ($\text{Na}^+(g) + \text{Cl}^-(g) \rightarrow \text{NaCl}(s)$).

Electronegativity (EN)

The relative ability of a bonded atom to attract shared electron pairs toward itself, rated on the Pauling scale from $0.7$ (for $\text{Fr}$) to $4.0$ (for $\text{F}$).

Resonance Hybrid

The true time-averaged electronic structure of a molecule that is best described as a composite blend of multiple contributing Lewis structures differing solely in the placement of electrons.

Formal Charge

The hypothetical charge an atom would possess in a molecule if all bonding electrons were shared equally, calculated using $\text{Formal Charge} = V - \left(L + \frac{1}{2}B\right)$, where $V$ is valence electrons, $L$ is lone pair electrons, and $B$ is shared bonding electrons.

Expanded Valence Shell

An exception to the octet rule where a central nonmetal atom from Period 3 or higher accommodates more than eight valence electrons by utilizing empty, accessible $d$-orbitals.

Incomplete Octet

A bonding situation observed in electron-deficient compounds of certain Group 13 elements (such as $\text{BF}_3$) where the central atom is stable with fewer than eight valence electrons.

VSEPR Model

The Valence Shell Electron Pair Repulsion model, which rationalizes molecular geometries by asserting that regions of high electron concentration (bonds and lone pairs) position themselves as far apart as possible to minimize electron-electron repulsion.

Trigonal Bipyramidal Geometry

The electron-pair arrangement adopted by five regions of electron density around a central atom, exhibiting equatorial bond angles of $120^\circ$ and axial-equatorial angles of $90^\circ$.

Seesaw Molecular Geometry

The molecular shape of a molecule with five electron domains (one equatorial lone pair and four bonding pairs), in which the lone pair occupies an equatorial site to minimize $90^\circ$ lone pair-bonding pair repulsions.

T-Shaped Molecular Geometry

The molecular shape adopted by a molecule with five electron domains consisting of three bonding pairs and two equatorial lone pairs (such as $\text{ClF}_3$ or $\text{BrF}_3$).

Octahedral Geometry

The geometry adopted by six electron domains around a central atom where all adjacent bond angles are mutually perpendicular at $90^\circ$ (and opposite bonds are $180^\circ$).

Square Pyramidal Molecular Geometry

The molecular shape resulting from six electron domains around a central atom that consists of five bonding pairs and one lone pair (such as $\text{BrF}_5$).

Square Planar Molecular Geometry

The molecular shape that results when an octahedral electron-group arrangement possesses four bonding pairs and two lone pairs oriented directly opposite each other ($180^\circ$ apart) to minimize lone pair-lone pair interactions (such as $\text{XeF}_4$).