CEM 141 Chapter 2 Comprehensive Study Guide

Vocabulary practice flashcards covering wave and particle properties of electromagnetic radiation, atomic spectra, quantum mechanical models, electron configurations, and periodic trends from CEM 141 Chapter 2.

Wavelength ($\lambda$)

The distance between consecutive wave crests or troughs, measured in meters ($\text{m}$). Shorter crest-to-crest spacing corresponds to higher frequency and higher photon energy.

Frequency ($\nu$)

The number of complete wave cycles passing a fixed point each second, measured in reciprocal seconds ($\text{s}^{-1}$) or Hertz ($\text{Hz}$). More cycles per second corresponds to higher frequency.

Amplitude

The height of a wave crest from its centerline. In the classical wave model, greater amplitude corresponds to greater intensity or brightness; in the modern quantum model, brightness depends on the number of photons per second.

Wave Equation

The fundamental wave relationship $c = \lambda\nu$, where $c$ is the speed of light ($3.00 \times 10^8\,\text{m/s}$ in a vacuum), $\lambda$ is wavelength in meters, and $\nu$ is frequency in $\text{s}^{-1}$ or $\text{Hz}$.

Electromagnetic Spectrum Ranking (Increasing Frequency and Energy)

The order of electromagnetic radiation types from lowest to highest frequency and energy (and decreasing wavelength): Radio < Microwave < Infrared (IR) < Visible < Ultraviolet (UV) < X-ray < Gamma Ray.

Visible Light Spectrum

The visible portion of electromagnetic radiation, ordered from lowest energy and longest wavelength to highest energy and shortest wavelength: Red ($700\,\text{nm}$) \rightarrow Orange \rightarrow Yellow \rightarrow Green \rightarrow Blue \rightarrow Indigo \rightarrow Violet ($400\,\text{nm}$).

Diffraction and Interference Patterns

Alternating bright and dark bands produced when light passes through narrow double slits or around obstacles comparable to its wavelength, serving as evidence for wave behavior via constructive and destructive interference.

Photoelectric Effect

The emission of electrons from a clean metal surface in a vacuum when struck by light at or above a specific threshold frequency ($\nu_0$).

Threshold Frequency ($\nu_0$)

The minimum frequency of incident light required to eject electrons from a metal surface. Below $\nu_0$, zero electrons are emitted regardless of beam intensity or duration.

Work Function ($\Phi$)

The minimum electrostatic binding energy holding an electron to the metal surface that a single incident photon must overcome ($E \ge \Phi$) to eject that electron.

Photon

A discrete packet (quantum) of electromagnetic energy that interacts with an electron in a metal surface in an instantaneous 1-to-1 event.

Energy of a Photon Equation

The formula $E = h\nu = \frac{hc}{\lambda}$, where $E$ is energy in Joules ($\text{J}$), $h$ is Planck's constant ($6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$), and $c$ is the speed of light ($3.00 \times 10^8\,\text{m/s}$).

Light Intensity (Quantum Model)

The number of photons arriving per second; when $\nu > \nu_0$, higher intensity increases the rate of electrons ejected per second without changing the kinetic energy per electron.

Atomic Emission Spectrum

A series of discrete, sharp bright colored lines on a dark background, produced when excited gaseous atoms relax as electrons transition from higher to lower energy levels and emit photons.

Atomic Absorption Spectrum

A series of dark lines on a continuous rainbow background, formed when white light passes through a cool elemental gas and electrons absorb photons matching transition gaps to higher bound levels.

Quantized Energy Levels

Discrete, fixed electronic energy states within an atom ($\Delta E = h\nu$), evidenced by the observation of sharp spectral lines rather than a continuous rainbow.

de Broglie Wavelength

The wavelength associated with matter, given by $\lambda = \frac{h}{m \cdot v}$, where $m$ is mass in kilograms ($\text{kg}$) and $v$ is velocity in $\text{m/s}$.

Heisenberg Uncertainty Principle

The quantum physical limit given by $\Delta(mv) \cdot \Delta x > \frac{h}{2\pi}$, stating that the exact position ($x$) and momentum ($mv$) of an electron cannot be simultaneously determined.

Atomic Orbital

A mathematical wave function ($\psi$) whose square ($\psi^2$) represents the 3D probability density of finding an electron, commonly drawn as a boundary surface enclosing $90\%$ probability.

s Orbital

A spherically symmetric atomic orbital centered on the nucleus, possessing one possible spatial orientation per energy level.

p Orbital

A dumbbell-shaped atomic orbital with two lobes separated by a planar nodal surface at the nucleus, existing in three mutually perpendicular orientations ($p_x$, $p_y$, $p_z$).

Aufbau Principle

The rule stating that electrons fill atomic orbitals in order of increasing energy: $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p$.

Pauli Exclusion Principle

The principle stating that an orbital can hold a maximum of 2 electrons, which must have opposite (paired) spins.

Hund's Rule

The rule stating that when filling degenerate orbitals within the same subshell, electrons occupy each orbital singly with parallel spins before pairing up.

Chromium Anomalous Electron Configuration

The ground-state configuration of Chromium ($Z = 24$), written as $[\text{Ar}]\,4s^1 3d^5$ because half-filled subshells offer greater stability than the expected $[\text{Ar}]\,4s^2 3d^4$.

Copper Anomalous Electron Configuration

The ground-state configuration of Copper ($Z = 29$), written as $[\text{Ar}]\,4s^1 3d^{10}$ because a completely filled $d$ subshell provides enhanced stability over $[\text{Ar}]\,4s^2 3d^9$.

Valence Electrons

Electrons residing in the outermost principal shell (highest $n$) and in unfilled $d$ subshells, which participate directly in chemical bonding.

Core Electrons

Electrons occupying inner, completely filled electron shells; they are stable, chemically inert, and shield valence electrons from the positive nuclear charge.

Dalton Model

An atomic model depicting atoms as solid, indivisible, and indestructible spheres based on the conservation of mass and definite proportions; unable to explain static charges, subatomic particles, or isotopes.

Thomson Model

The 'plum pudding' model depicting a diffuse sphere of positive charge containing embedded negative electrons, derived from cathode ray tube experiments; unable to account for large-angle alpha particle deflections.

Rutherford Model

An atomic model featuring a tiny, dense, positively charged nucleus surrounded by electrons in mostly empty space, supported by the gold foil experiment; failed to explain orbital stability and discrete spectra.

Bohr Model

An atomic model in which electrons orbit the nucleus in fixed, quantized circular paths at specific energy levels to explain hydrogen emission; failed for multi-electron atoms and violated the uncertainty principle.

Schrödinger Quantum Mechanical Model

The current accepted atomic model treating electrons as 3D standing matter waves characterized by orbital probability densities ($\psi^2$), supported by wave-particle duality and electron diffraction.

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

The relationship $Z_{\text{eff}} \approx Z - S$, where $Z$ is total nuclear charge (protons) and $S$ is the shielding constant produced primarily by core electrons.

Coulomb's Law (Atomic Scale)

The electrostatic relationship $F \propto \frac{q_1 \cdot q_2}{r^2}$, stating that attraction increases with higher effective nuclear charge ($Z_{\text{eff}}$) and decreases as distance squared ($r^2$) increases.

First Ionization Energy Trend

The periodic trend where ionization energy increases across a period due to increasing $Z_{\text{eff}}$ pulling electrons tighter, and decreases down a group due to larger principal quantum shells ($n$) and greater distance ($r$).

Successive Ionization Energies

Ionization energies that increase gradually as successive valence electrons are removed, followed by a massive, abrupt jump when removing the first core electron from a lower principal shell ($n - 1$).

Cation vs. Parent Atom Radius

Cations are smaller than their parent neutral atoms because removing electrons decreases electron-electron repulsion and often completely vacates the outermost quantum shell.

Anion vs. Parent Atom Radius

Anions are larger than their parent neutral atoms because adding electrons increases electron-electron repulsion, expanding the electron cloud.

Isoelectronic Series

A group of chemical species containing the same number of electrons and identical configurations (e.g., $\text{O}^{2-} > \text{F}^- > \text{Ne} > \text{Na}^+ > \text{Mg}^{2+} > \text{Al}^{3+}$), where radius decreases steadily as atomic number ($Z$) increases.