Chapter 12 Quantum Mechanics and Atomic Theory

Flashcards covering key vocabulary terms, quantum numbers, equations, and principles from Chapter 12: Quantum Mechanics and Atomic Theory.

Wavelength ($\lambda$)

The distance between adjacent crests of a wave, expressed in meters ($\text{m}$).

Frequency ($\nu$)

The number of wave crests passing through a given point per second, measured in Hertz ($\text{Hz}$) or $\text{s}^{-1}$.

Speed of Light ($c$)

The constant speed at which a wave crest travels in a vacuum, independent of its frequency, given by $c = \lambda \nu$.

Amplitude

The maximum height of a wave measured above its center line.

Constructive Interference

Wave interference occurring when a crest of one wave meets a crest of another wave, resulting in the addition of their amplitudes.

Destructive Interference

Wave interference occurring when a crest of one wave meets a trough of another wave, causing the two waves to cancel each other out.

Black-body Radiation

The electromagnetic radiation emitted by all non-reflective objects (black bodies), peaking at a characteristic frequency that shifts to shorter wavelengths with increasing temperature.

Ultraviolet Catastrophe

The false prediction of classical electromagnetic theory that the intensity of black-body radiation would increase indefinitely with decreasing wavelength.

Photon

A stream of quantized light particles postulated by Max Planck, each carrying energy given by Planck's equation $E = h\nu = \frac{hc}{\lambda}$.

Atomic Absorption Lines

Discontinuous absorption spectra produced when matter absorbs photons matching the energy difference between its final and initial states ($E_{photon} = E_f - E_i$).

Atomic Emission Lines

Discontinuous emission spectra produced when excited atoms emit energy as photons to relax to lower energy levels ($E_{photon} = E_i - E_f$).

Hydrogen-like Species

The hydrogen atom and single-electron ions, such as $\text{H}$, $\text{He}^+$, $\text{Li}^{2+}$, and $\text{Be}^{3+}$.

Bohr Model

A model for hydrogen-like species in which an electron revolves around the nucleus in allowed circular orbits of specified radii determined by quantum number $n$.

Balmer Series

A set of hydrogen emission lines produced when an electron relaxes from a higher level to the $n = 2$ level.

Lyman Series

A set of hydrogen emission lines produced when an electron relaxes from a higher level to the $n = 1$ level.

Ionization Energy of Hydrogen

The energy required to absorb a photon that completely removes an electron from its ground state ($n = 1$) to an isolated stationary state ($n = \infty$), given by $E = R_H$.

De Broglie Wave-Particle Duality

The concept that material particles display wave-like properties with a wavelength inversely proportional to momentum, given by $\lambda = \frac{h}{p} = \frac{h}{m u}$.

Electron Diffraction

The creation of a wave interference diffraction pattern when electrons are scattered by a thin metal foil.

Heisenberg's Uncertainty Principle

The fundamental limit on simultaneously measuring a particle's position ($x$) and momentum ($p$) with absolute precision, expressed as $\Delta x \Delta p \ge \frac{h}{4\pi}$.

Wave Function ($\psi$)

A function obtained by solving the Schrödinger equation that describes a particle exhibiting quantum wave-like properties.

Probability Density ($\psi^2$)

The value $\psi^2(x)$ representing the probability of finding a quantum particle at a specific position $x$.

Radial Node

A spherical surface on which the probability density $\psi^2$ is zero, occurring where the radial wave function $R(r) = 0$.

Angular Node

A non-spherical node occurring at angles satisfying $Y(\theta, \phi) = 0$.

Principal Quantum Number ($n$)

The quantum number ($n = 1, 2, 3, \dots, \infty$) determining orbital size and the overall shell energy in single-electron species.

Angular Momentum Quantum Number ($l$)

The quantum number ($l = 0, 1, 2, \dots, n-1$) defining the subshell and geometric shape of an atomic orbital.

Magnetic Quantum Number ($m_l$)

The quantum number ($m_l = -l, \dots, 0, \dots, +l$) designating the three-dimensional orientation of an orbital in space.

Electron Spin Quantum Number ($m_s$)

The fourth quantum number ($m_s = +\frac{1}{2}$ or $m_s = -\frac{1}{2}$) indicating an electron's intrinsic magnetic spin direction.

Shielding Effect

The reduction in magnetic and electrostatic attraction between outer electrons and the nucleus caused by inner electrons repelling the outer electrons.

Pauli Exclusion Principle

The quantum rule stating that no two electrons in an atom can have the exact same set of all four quantum numbers.

Hund's Rule

The principle stating that electrons occupy degenerate orbitals singly with parallel spins before pairing up to maximize unpaired electrons.

Aufbau Process

The hypothetical process of building up an electron configuration by progressively adding protons and electrons into available orbitals of lowest energy.

n + l Rule

The rule stating that electronic subshells with lower $n + l$ values are filled before higher ones, and if two subshells have equal $n + l$, the lower $n$ subshell fills first.