The Quantum-Mechanical Model of the Atom: Part I

Vocabulary practice flashcards covering Chapter 8 (Part I): The Quantum-Mechanical Model of the Atom from General Chemistry (CHM 2045C).

Determinacy

The classical physics principle that the present physical conditions (position, velocity, and acting forces) of a particle completely determine its future path along a definite, predictable trajectory.

Indeterminacy

The quantum-mechanical principle that because the exact position and velocity of an electron cannot be simultaneously known, its future trajectory cannot be predicted, allowing only probability distributions to be described.

Electromagnetic Radiation

A form of energy characterized by oscillating waves composed of electric and magnetic fields that propagate through space in mutually perpendicular planes.

Electric Field

A region of space where an electrically charged particle experiences a force.

Magnetic Field

A region of space where a magnetized particle experiences a force.

Speed of Light ($c$)

The constant speed at which all electromagnetic waves travel through space, equal to $3.00 \times 10^8\,\text{m/s}$.

Amplitude

The vertical height of a wave, measured from the node to the crest or from the node to the trough, which determines the intensity or brightness of the light.

Wavelength ($\lambda$)

The physical distance covered by a wave between adjacent identical points, such as from one crest to the next crest, one trough to the next trough, or between alternate nodes.

Frequency ($\nu$)

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

Electromagnetic Spectrum

The complete continuum of all wavelengths of electromagnetic radiation, encompassing low-energy radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and high-energy gamma rays.

Constructive Interference

The interaction of two or more waves that are in phase, adding their amplitudes together to produce a wave of greater amplitude.

Destructive Interference

The interaction of two or more waves that are out of phase, where the crest of one aligns with the trough of another, canceling each other out.

Diffraction

The bending or spreading of traveling waves around an obstacle or when passing through an opening that is comparable in size to the wavelength.

Photoelectric Effect

The phenomenon in which electrons are ejected from the surface of a metal when light of sufficiently high frequency shines upon it.

Threshold Frequency

The minimum frequency of incident light required to dislodge and eject electrons from a given metal surface, below which no electrons are emitted regardless of light intensity.

Photon

A discrete, quantized packet of light energy whose energy is directly proportional to its frequency ($E = h\nu$) and inversely proportional to its wavelength ($E = \frac{hc}{\lambda}$).

Planck's Constant ($h$)

The fundamental physical proportionality constant relating a photon's energy to its frequency, having a value of $6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$.

Binding Energy ($\phi$)

The minimum threshold energy required to liberate an electron from the surface of a metal atom in the photoelectric effect.

Emission Spectrum

A noncontinuous series of discrete wavelengths of light produced when light emitted by energized atoms or molecules is separated through a prism, serving as a unique identifier for that element.

Rydberg Constant ($R$)

An empirical constant in the Rydberg equation for hydrogen emission lines, equal to $1.097 \times 10^7\,\text{m}^{-1}$.

Stationary States

Specific, stable, non-radiating circular orbits in Niels Bohr's atomic model where an electron can reside at fixed distances from the nucleus with quantized energy levels.

de Broglie Wavelength

The wavelength associated with any moving particle of matter, determined by dividing Planck's constant by the particle's momentum ($\lambda = \frac{h}{mv}$).

Complementary Properties

Two mutually exclusive physical properties—such as wave nature (interference) and particle nature (position)—where measuring or knowing one property more precisely reduces knowledge of the other.

Heisenberg Uncertainty Principle

A fundamental quantum limit stating that the product of the uncertainties in position and velocity for a particle is inversely proportional to its mass ($\Delta x \times m\Delta v \ge \frac{h}{4\pi}$).

Schrödinger's Equation

The fundamental quantum-mechanical equation ($H\psi = E\psi$) that calculates the energy states and spatial probability distributions of electrons in an atom.

Wave Function ($\psi$)

A mathematical solution to Schrödinger's equation that describes the wave nature and quantum state of an electron in an atom.

Probability Density ($\psi^2$)

The square of the wave function at a specific point in space, representing the probability per unit volume of finding an electron at that point.

Orbital

A three-dimensional probability distribution map derived from the square of the wave function ($\psi^2$), defining the region in an atom where an electron is most likely to be located.

Principal Quantum Number ($n$)

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

Angular Momentum Quantum Number ($l$)

An integer quantum number ranging from $0$ to $n - 1$ that dictates the geometric shape of an atomic orbital, designated by the letters $s$ ($l=0$), $p$ ($l=1$), $d$ ($l=2$), and $f$ ($l=3$).

Magnetic Quantum Number ($m_l$)

An integer quantum number ranging from $-l$ to $+l$ (including zero) that determines the spatial orientation of an orbital within a sublevel.

Spin Quantum Number ($m_s$)

A quantum number specifying the orientation of an electron's intrinsic angular momentum (spin), which has only two quantized values: $+\frac{1}{2}$ ("spin up") and $-\frac{1}{2}$ ("spin down").

Sublevel (Subshell)

A division of a principal energy level containing a set of orbitals that share identical values of both the principal quantum number ($n$) and the angular momentum quantum number ($l$).

Radial Distribution Function

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

Node

A point, plane, or spherical surface within a wave function or orbital where the wave amplitude equals zero, meaning the probability density ($\psi^2$) of finding an electron drops to zero.

Phase of an Orbital

The algebraic sign (positive or negative) of the mathematical wave function ($\psi$) across different spatial regions of an orbital.