Quantum Mechanics and Electronic Structure

Comprehensive vocabulary flashcards covering wave properties, quantum theory, atomic spectra, quantum numbers, electron configurations, and periodic trends from Chapter 7.

Electromagnetic Radiation

The emission and transmission of energy in the form of electromagnetic waves.

Wavelength ($\lambda$)

The distance between identical points on successive waves.

Amplitude

The vertical distance from the midline of a wave to a peak or trough.

Frequency ($\nu$)

The number of waves that pass through a particular point in a second, measured in Hertz ($\text{Hz} = 1\,\text{cycle/s}$).

Speed of Light ($c$)

The constant speed of electromagnetic radiation in a vacuum, equal to $3.00 \times 10^8\,\text{m/s}$, relating wavelength and frequency by $\lambda \times \nu = c$.

Continuous Spectrum

A spectrum that contains all wavelengths of visible light from red to violet without gaps, such as the emission from a heated solid or an incandescent light bulb.

Line Spectrum

A spectrum produced by excited atoms in the gas phase resulting from the emission of light only at specific, discrete wavelengths.

Ultraviolet Catastrophe

The failure of classical physics to predict blackbody radiation, incorrectly asserting that heated solids would emit light with intensity that approached infinity at shorter (ultraviolet) wavelengths.

Quantized

Restricted to having only certain discrete, specific allowed values or amounts rather than an arbitrary continuous range.

Planck's Constant ($h$)

The fundamental constant of proportionality relating the energy of a quantum to its frequency ($E = h\nu$), equal to $6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$.

Photoelectric Effect

The phenomenon in which electrons are ejected from the surface of a metal when light of sufficient frequency strikes it.

Threshold Frequency

The minimum frequency of incident light below which no electrons are ejected from a metal surface, regardless of the light's intensity.

Photon

A quantized packet or particle of light energy, where the energy of a single quantum is given by $E = h\nu$.

Work Function ($\Phi$)

The minimum amount of energy required to remove an electron from the surface of a metal.

Stationary States

The stable circular orbits in the Bohr model located at fixed distances from the nucleus in which an electron does not radiate energy.

Ground State

The lowest-energy, most stable orbit or electronic state available to an atom ($n = 1$ for hydrogen).

Excited State

An unstable state of higher energy into which an electron transitions after absorbing energy.

Rydberg Constant ($R_H$)

A fundamental constant equal to $2.18 \times 10^{-18}\,\text{J}$ used in calculating energy levels and spectral transitions of hydrogen.

Lyman Series

The series of emission lines in the hydrogen spectrum resulting from electron transitions down to the $n_f = 1$ energy level, occurring in the ultraviolet region.

Balmer Series

The series of emission lines in the hydrogen spectrum resulting from electron transitions down to the $n_f = 2$ energy level, producing visible and ultraviolet light.

De Broglie Wavelength

The wavelength associated with a particle of mass $m$ moving at velocity $v$, calculated using $\lambda = \frac{h}{mv}$.

Constructive Interference

An interaction where waves are in phase (aligning peak-to-peak), producing an additive increase in amplitude.

Destructive Interference

An interaction where waves are out of phase (aligning peak-to-trough), causing their amplitudes to cancel out.

Diffraction

The bending and spreading of waves as they pass through a slit or around an obstacle comparable in size to their wavelength.

Heisenberg Uncertainty Principle

The principle stating that it is impossible to know simultaneously both the exact position ($x$) and momentum ($p = mv$) of a particle, governed by $\Delta x \cdot m\Delta v \ge \frac{h}{4\pi}$.

Schrödinger Equation

A fundamental mathematical wave equation describing the probability distribution and regions of space (electron density) where an electron is likely to be found.

Atomic Orbital

A three-dimensional region of space around the nucleus defined by the wave function where there is a high probability of finding an electron.

Principal Quantum Number ($n$)

The quantum number ($n = 1, 2, 3, \dots$) that designates the main energy level or shell and defines the relative average distance of the electron from the nucleus.

Angular Momentum Quantum Number ($l$)

The quantum number ($l = 0, 1, \dots, n-1$) that defines the shape of the orbital and identifies the subshell ($s, p, d, f$).

Magnetic Quantum Number ($m_l$)

The quantum number with integer values from $-l$ to $+l$ that specifies the orientation of an orbital in three-dimensional space.

Electron Spin Quantum Number ($m_s$)

The quantum number with values of $+\frac{1}{2}$ or $-\frac{1}{2}$ that describes the intrinsic magnetic spin orientation of an electron.

Pauli Exclusion Principle

The rule stating that no two electrons in an atom can have identical values for all four quantum numbers ($n, l, m_l, m_s$), limiting any single orbital to two electrons with opposite spins.

Aufbau Principle

The procedure of building up an atom's electron configuration by adding electrons one at a time into the lowest-energy available orbital.

Hund's Rule

The principle stating that the most stable electron arrangement in degenerate subshells is that with the greatest number of parallel spins.

Degenerate Orbitals

Atomic orbitals that possess identical energy levels.

Electron Penetration

The ability of an electron in an outer orbital to penetrate core electron density and experience a greater attractive force from the nucleus, following the order $s > p > d$.

Paramagnetic

A condition of atoms or materials that contain one or more unpaired electrons, causing them to be attracted by an external magnetic field.

Diamagnetic

A condition of atoms or materials in which all electrons are paired, causing them to be weakly repelled by an external magnetic field.

Valence Electrons

Electrons residing in the highest principal energy level ($n$) for main-group elements, plus incompletely filled $(n-1)d$ subshells in transition metals, that are involved in bonding.

Core Electrons

The inner, non-valence electrons that occupy completely filled interior shells of an atom.

Isoelectronic

Species (atoms, cations, or anions) that have the exact same number of electrons and identical ground-state electron configurations.

Effective Nuclear Charge ($Z_{\text{eff}}$)

The net positive nuclear charge experienced by an outer electron, calculated approximately as the actual nuclear charge minus the shielding constant ($Z_{\text{eff}} \approx Z_{\text{actual}} - S$).

Electron Shielding

The reduction of electrostatic attraction between the positive nucleus and outer electrons caused by repulsive forces from inner-shell electrons.

Covalent Radius

Half the distance between the nuclei of two adjacent identical atoms bonded together in a molecule.

Ionization Energy ($IE$)

The minimum energy required to remove an electron from an isolated gaseous atom or ion in its ground state ($\text{energy} + \text{X}_{(g)} \rightarrow \text{X}^+_{(g)} + e^-$).

Electron Affinity ($EA$)

The energy change that occurs when an electron is accepted by an atom in the gaseous state to form an anion ($\text{X}_{(g)} + e^- \rightarrow \text{X}^-_{(g)}$).

Metallic Character

The extent to which an element displays the physical and chemical properties of metals, including conductivity, malleability, ductility, and the tendency to lose electrons.

Electron Sea Model

A bonding model for metals in which an array of positive metal cations is immersed in a shared, delocalized pool of freely moving valence electrons.