Chapter 2: The Quantum-Mechanical Model of the Atom Flashcards

Vocabulary flashcards covering key concepts, equations, and diagrams from Chapter 2: The Quantum-Mechanical Model of the Atom.

Electromagnetic Radiation

A form of energy composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field, moving through space at a constant speed of $3.00 \times 10^8 accession m/s$.

Amplitude

The height of a wave measured from node to crest or node to trough, which serves as an extensive physical measure of light intensity or brightness.

Wavelength ($\lambda$)

The distance covered by a wave from one crest to the next, one trough to the next, or between alternate nodes, which determines the color of light.

Frequency ($\nu$)

The number of waves or cycles that pass a given point in a specified period of time, expressed in units of hertz ($\text{Hz}$) or $\text{s}^{-1}$.

Constructive Interference

The interaction of waves that are in phase, resulting in them combining to form a wave with a larger amplitude.

Destructive Interference

The interaction of waves that are out of phase, causing them to cancel each other out.

Diffraction

The bending of traveling waves around an obstacle or opening in a barrier that is comparable in size to their wavelength.

Photoelectric Effect

The phenomenon in which electrons (photoelectrons) are emitted from the surface of a metal when light is shined upon it.

Threshold Frequency

The minimum frequency of light required to eject electrons from a metal surface, regardless of the light's intensity.

Photon

A packet or quantum of light energy whose energy is directly proportional to its frequency ($E = h\nu$) and inversely proportional to its wavelength.

Planck's Constant ($h$)

The proportionality constant relating the energy of a photon to its frequency, equal to $6.626 \times 10^{-34},\text{J}\times\text{s}$.

Binding Energy ($\phi$)

The threshold amount of energy required to remove an electron from an atom or metal surface.

Emission Spectrum

A non-continuous pattern of specific wavelengths of light produced when energy-absorbing atoms or molecules emit light through a prism.

Bohr Model of the Atom

An atomic model where electrons revolve around the nucleus in fixed concentric orbits (stationary states) and emit light photons when transitioning between orbits.

Ground State

The most stable, lowest energy state of a particle or atom.

Excited State

Any energy state of a particle or atom that is higher in energy than its ground state.

Electron Transition

The movement of an electron from one energy state to another within an atom.

Schrödinger's Equation ($\hat{H}\psi = E\psi$)

A fundamental quantum-mechanical equation whose solutions produce wave functions ($\psi$) to calculate the probability of finding an electron with a specific energy at a given location in an atom.

Orbital

A probability distribution map representing the region in space where an electron is most likely to be found, represented by the square of the wave function ($\psi^2$).

Principal Quantum Number ($n$)

An integer quantum number ($n \ge 1$) that specifies the principal energy level, overall size, and energy of an orbital.

Angular Momentum Quantum Number ($l$)

The quantum number that determines the shape of an atomic orbital, taking integer values from $0$ to $(n - 1)$.

Magnetic Quantum Number ($m_l$)

An integer quantum number specifying the orientation of an orbital in space, with values ranging from $-l$ to $+l$.

Spin Quantum Number ($m_s$)

The quantum number describing the orientation of an electron's spin in an atomic orbital, equal to $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down).

Principal Shell

A collection of atomic orbitals that share the same principal quantum number ($n$).

Subshell (Sublevel)

A division of a principal energy level containing orbitals that have the same values for both $n$ and $l$.

Probability Density ($\psi^2$)

The mathematical square of the wave function that gives the probability of finding an electron at a specific point in space.

Node

A point or region in a wave function or orbital where the probability density ($\psi^2$) drops to zero.

Radial Distribution Function

A plot representing the total probability of finding an electron within a thin spherical shell at a distance $r$ from the nucleus, which peaks at $52.9\,\text{pm}$ for the hydrogen 1s orbital.

s Orbital

A spherically shaped atomic orbital corresponding to $l = 0$, containing $(n - 1)$ nodes.

p Orbitals

Two-lobed, dumbbell-shaped atomic orbitals corresponding to $l = 1$, oriented along the x, y, or z axes with a node at the nucleus.

d Orbitals

A set of five atomic orbitals corresponding to $l = 2$, four of which are four-lobed and one of which is two-lobed with a toroid ring.

f Orbitals

A set of seven atomic orbitals corresponding to $l = 3$, primarily featuring eight-lobed shapes.

Wave-Matter Duality

The concept that subatomic matter, such as an electron, exhibits both particulate characteristics (mass, volume) and wave-like energy behavior depending on experimental conditions.

Electromagnetic Spectrum

The complete spectrum of electromagnetic radiation arranged by wavelength and frequency, ranging from high-energy gamma rays to low-energy radio waves.