Principles of Chemistry I: Line Spectra and Quantum Theory

Line Spectra

Discrete wavelengths emitted by excited gases.

Continuous Spectrum

Unbroken series of wavelengths from heated solids.

Photon

Quantum of light with energy proportional to frequency.

Balmer Equation

Relates visible wavelengths of hydrogen to integers.

Rydberg Formula

Predicts all hydrogen emission lines using integers.

Bohr Model

Explains hydrogen emission spectra using quantized orbits.

Ground State

Lowest energy state of an atom (n=1).

Excited State

Higher energy state of an atom (n>1).

Energy Difference (ΔE)

Energy change when electron transitions between orbits.

Rydberg Constant (R∞)

Constant used in Rydberg formula (1.097 × 10⁷ m⁻¹).

Quantum Numbers

Integer values defining electron states in atoms.

Planck's Constant

Fundamental constant relating energy and frequency.

Electromagnetic Spectrum

Range of all types of electromagnetic radiation.

Wavelength (λ)

Distance between consecutive peaks of a wave.

Niels Bohr

Scientist who developed the Bohr model of the atom.

Classical Electromagnetism

Theory predicting continuous radiation from accelerating charges.

Quantization

Concept that energy levels are discrete, not continuous.

Energy Absorption

Process when an electron moves to a higher orbit.

Energy Emission

Process when an electron falls to a lower orbit.

Infrared Radiation

Part of the electromagnetic spectrum with longer wavelengths.

Electron Mass

Mass of an electron, fundamental in energy calculations.

Electron Charge

Charge of an electron, fundamental in atomic interactions.

Wave-Particle Duality

Concept that particles exhibit both wave and particle properties.

Three-Dimensional Wave Functions

Mathematical functions describing electron probability distributions.

Johann Balmer

Derived empirical equation for hydrogen's visible wavelengths.

Johannes Rydberg

Generalized Balmer's work for all hydrogen emission lines.

Classical Mechanics

Physics theory inadequate for atomic and subatomic levels.

Nobel Prize in Physics

Awarded to Bohr for contributions to atomic theory.

Quantum Mechanical Description

Uses wave functions to describe electron probability distributions.

De Broglie Wavelength

Wavelength associated with a particle's momentum.

Planck's Constant (h)

Fundamental constant relating energy and frequency.

Wave Nature of Electrons

Electrons can exhibit interference patterns like waves.

Heisenberg Uncertainty Principle

Limits simultaneous measurement of position and momentum.

Schrödinger Equation

Mathematical equation describing quantum state evolution.

Wave Function (ψ)

Mathematical function representing quantum state of a particle.

Probability Density

Square of wave function magnitude indicating electron location likelihood.

Principal Quantum Number (n)

Indicates energy level and size of an orbital.

Atomic Orbital

Region where an electron is likely to be found.

Angular Momentum Quantum Number (ℓ)

Defines the shape of an orbital.

Subshell

Group of orbitals with the same angular momentum quantum number.

Orbital Energies

Energy increases in order: s < p < d < f.

Radial Nodes

Points where electron probability density is zero.

Magnetic Quantum Number

Specifies orientation of an orbital in space.

Electron Configuration

Distribution of electrons among atomic orbitals.

Interference Pattern

Result of wave superposition, showing electron wave behavior.

Hamiltonian Operator (Ĥ)

Represents total energy in the Schrödinger equation.

Energy Quantization

Electrons can only occupy discrete energy levels.

Standing Wave

Wave pattern that remains stationary in space.

Electron Density

Probability of finding an electron in a region.

Dumbbell Shape

Shape of p orbitals indicating electron distribution.

Spherical Shape

Shape of s orbitals indicating electron distribution.

Complex Probability Amplitudes

Mathematical representation of electron probabilities.

Energy Level Transition

Jump between quantized energy levels without intermediate states.

Electron Repulsion

Causes energy differences in subshells with multiple electrons.

1s Orbital

First shell with n=1, ℓ=0, no nodes.

2s Orbital

Second shell with n=2, ℓ=0, one node.

3s Orbital

Third shell with n=3, ℓ=0, two nodes.

Magnetic Quantum Number (mℓ)

Specifies orbital orientation in space.

Value Range of mℓ

mℓ = -ℓ to +ℓ values.

Degenerate Energy Levels

Orbitals with same n have identical energy.

Aufbau Principle

Electrons fill lowest energy orbitals first.

Spin Quantum Number (ms)

Describes electron spin states, +½ or -½.

Pauli Exclusion Principle

No two electrons can have identical quantum numbers.

Orbital Diagrams

Visual representations of electron configurations.

Hund's Rule

Maximize unpaired electrons in degenerate orbitals.

Valence Electrons

Electrons in the outermost shell.

Core Electrons

Electrons in inner shell orbitals.

Abbreviated Electron Configuration

Uses noble gas notation for core electrons.

Transition Metals

Elements filling d subshells after scandium.

Electron Configuration Exceptions

Cu and Cr have unique electron arrangements.

f Orbitals

Seven orbitals with capacity for 14 electrons.

Main Group Elements

Last electron enters s or p orbital.

Electron Capacity of d Orbitals

Five d orbitals can hold 10 electrons.

Electron Capacity of f Orbitals

Seven f orbitals can hold 14 electrons.

n Value

Principal quantum shell number.

ℓ Value

Angular momentum quantum number.

Electron Pairing

Electrons in the same orbital must have opposite spins.

Degenerate Orbitals

Orbitals within the same subshell have same energy.

Electron-Electron Interactions

Alter energy levels in multi-electron atoms.

Electron Configuration for Gallium

[Ar]4s2 3d10 4p1, three valence electrons.

Gallium (Ga)

Has three valence electrons: 4s2 and 4p1.

Vanadium (V)

Has five valence electrons: 4s2 and 3d3.

Inner Transition Elements

Elements where last electron occupies an f orbital.

Promethium (Pm)

Has seven valence electrons: 6s2 and 4f5.

Cation

Positively charged ion formed by electron loss.

Anion

Negatively charged ion formed by electron gain.

Ionization Energy (IE)

Energy needed to remove an electron from an atom.

First Ionization Energy (IE1)

Energy to remove the most loosely bound electron.

Successive Ionization Energies

Energy required for sequential electron removals.

Electron Affinity (EA)

Energy change when an electron is added to an atom.

Covalent Radius

Half the distance between two bonded nuclei.

Effective Nuclear Charge (Zeff)

Net positive charge experienced by an electron.

Ionic Radius

Size of an ion compared to its parent atom.

Isoelectronic

Atoms or ions with identical electron configurations.

Deviations in Ionization Energy

Exceptions to expected trends in ionization energy.

Electron Affinity Trends

EA becomes more negative across a period.

Noble Gases

Group 18 elements with filled electron shells.

Group 2 Elements

Have filled ns subshell, affecting electron affinity.

Group 15 Elements

Half-filled np subshell affects electron affinity.

Atomic Size

Radius of atoms and ions varies periodically.