Quantum-Mechanical Model and Electronic Structure of the Atom

Vocabulary practice flashcards for Unit 2A Chapter 3 covering light characteristics, wave-matter duality, quantum numbers, orbital shapes, and atomic energy transitions.

Wave-Matter Duality

The principle that microscopic matter, such as electrons, exhibits both energy-like wave properties and particulate matter properties (having mass and occupying space) depending on experimental conditions.

Quantum Mechanics

The atomic model that accounts for the wave-particle duality and probabilistic behavior of electrons in atoms.

Heisenberg Uncertainty Principle

The principle stating that it is impossible to know both the exact position and path of an electron simultaneously, defining it instead as a spread-out cloud of probability.

Schroedinger's Equation

The wave equation $H\psi = E\psi$ used to calculate the probability of finding an electron with a specific energy at a given location in an atom.

Orbital

A probability distribution map (represented by a plot of distance versus $\psi^2$) indicating the region in space where an electron is most likely to be found.

Principal Quantum Number ($n$)

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

Angular Momentum Quantum Number ($l$)

The quantum number with integer values from $0$ to $(n - 1)$ that specifies the shape or sublevel of an orbital ($s, p, d, f$).

Magnetic Quantum Number ($m_l$)

An integer quantum number ranging from $-l$ to $+l$ that specifies the spatial orientation of an orbital relative to other orbitals.

Spin Quantum Number ($m_s$)

The quantum number that specifies the direction of the electron's spin orientation within an orbital.

Principal Level and Sublevel Organization

The hierarchical structure of atomic electron levels where level $n$ contains $n$ sublevels, $n^2$ orbitals, and a maximum of $2n^2$ electrons.

Pauli Exclusion Principle

The rule stating that an orbital can hold a maximum of 2 electrons with opposing spins.

Probability Density Function

A function representing the total probability of finding an electron at a specific point in space, proportional to $\psi^2$.

Node

A point or surface in an orbital where the probability density of finding an electron is zero.

$s$ Orbital

A spherical orbital corresponding to $l = 0$, containing 1 orbital per principal energy level and possessing $(n - 1)$ nodes.

$p$ Orbital

A dumbbell-shaped, two-lobed orbital set corresponding to $l = 1$, consisting of 3 mutually perpendicular orbitals ($p_x, p_y, p_z$) holding up to 6 electrons.

$d$ Orbital

A set of 5 orbitals ($d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}, d_{z^2}$) corresponding to $l = 2$ present in energy levels $n \ge 3$, holding up to 10 electrons.

$f$ Orbital

A set of 7 complex, mainly eight-lobed orbitals corresponding to $l = 3$ present in energy levels $n \ge 4$, holding a maximum of 14 electrons.

Electromagnetic Radiation

Energy consisting of mutually perpendicular oscillating electric and magnetic fields traveling through space at the speed of light ($c = 3.00 \times 10^8\,\text{m/s}$).

Amplitude ($A$)

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

Wavelength ($\lambda$)

The distance between adjacent crests, troughs, or alternate nodes of a wave, which determines its color.

Frequency ($\nu$)

The number of wave cycles passing a fixed point per unit time, expressed in Hertz ($\text{Hz}$) or $\text{s}^{-1}$.

Electromagnetic Spectrum

The full range of electromagnetic radiation organized by frequency and wavelength, spanning from low-energy radio waves to high-energy gamma rays.

Photoelectric Effect

The release of photoelectrons from a metal surface when light of a sufficient threshold frequency shines on it.

Binding Energy ($\phi$)

The threshold amount of energy required to detach an electron from the metal surface in the photoelectric effect.

Photon

A discrete, quantized packet of light energy defined by $\text{Energy} = h\nu = \frac{hc}{\lambda}$.

Planck's Constant ($h$)

A physical constant equal to $6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$ (or $6.636 \times 10^{-34}\,\text{J}\cdot\text{s}$) relating the energy of a photon to its frequency.

Emission Spectrum

The spectrum of light wavelengths emitted by an element or molecule when its excited electrons transition back to lower energy levels.

Line Spectrum

A noncontinuous emission spectrum containing distinct wavelengths characteristic of a specific element or molecule.

Bohr Model of the Atom

A model proposing that electrons travel in fixed circular orbits (stationary states) around the nucleus at quantized energy levels.

Hydrogen Energy Transitions

Quantized electronic shifts between energy levels ($n$) in hydrogen described by $\Delta E = -2.18 \times 10^{-18}\,\text{J}\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$.

Wave-Matter Duality

The principle that microscopic matter, such as electrons, exhibits both energy-like wave properties and particulate matter properties (having mass and occupying space) depending on experimental conditions.

Quantum Mechanics

The atomic model that accounts for the wave-particle duality and probabilistic behavior of electrons in atoms.

Heisenberg Uncertainty Principle

The principle stating that it is impossible to know both the exact position and path of an electron simultaneously, defining it instead as a spread-out cloud of probability.

Schroedinger's Equation

The wave equation $H\psi = E\psi$ used to calculate the probability of finding an electron with a specific energy at a given location in an atom.

Orbital

A probability distribution map (represented by a plot of distance versus $\psi^2$) indicating the region in space where an electron is most likely to be found.

Principal Quantum Number ($n$)

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

Angular Momentum Quantum Number ($l$)

The quantum number with integer values from $0$ to $(n - 1)$ that specifies the shape or sublevel of an orbital ($s, p, d, f$).

Magnetic Quantum Number ($m_l$)

An integer quantum number ranging from $-l$ to $+l$ that specifies the spatial orientation of an orbital relative to other orbitals.

Spin Quantum Number ($m_s$)

The quantum number that specifies the direction of the electron's spin orientation within an orbital.

Principal Level and Sublevel Organization

The hierarchical structure of atomic electron levels where level $n$ contains $n$ sublevels, $n^2$ orbitals, and a maximum of $2n^2$ electrons.

Pauli Exclusion Principle

The rule stating that an orbital can hold a maximum of 2 electrons with opposing spins.

Probability Density Function

A function representing the total probability of finding an electron at a specific point in space, proportional to $\psi^2$.

Node

A point or surface in an orbital where the probability density of finding an electron is zero.

$s$ Orbital

A spherical orbital corresponding to $l = 0$, containing 1 orbital per principal energy level and possessing $(n - 1)$ nodes.

$p$ Orbital

A dumbbell-shaped, two-lobed orbital set corresponding to $l = 1$, consisting of 3 mutually perpendicular orbitals ($p_x, p_y, p_z$) holding up to 6 electrons.

$d$ Orbital

A set of 5 orbitals ($d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}, d_{z^2}$) corresponding to $l = 2$ present in energy levels $n \ge 3$, holding up to 10 electrons.

$f$ Orbital

A set of 7 complex, mainly eight-lobed orbitals corresponding to $l = 3$ present in energy levels $n \ge 4$, holding a maximum of 14 electrons.

Electromagnetic Radiation

Energy consisting of mutually perpendicular oscillating electric and magnetic fields traveling through space at the speed of light ($c = 3.00 \times 10^8\,\text{m/s}$).

Amplitude ($A$)

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

Wavelength ($\lambda$)

The distance between adjacent crests, troughs, or alternate nodes of a wave, which determines its color.

Frequency ($\nu$)

The number of wave cycles passing a fixed point per unit time, expressed in Hertz ($\text{Hz}$) or $\text{s}^{-1}$.

Electromagnetic Spectrum

The full range of electromagnetic radiation organized by frequency and wavelength, spanning from low-energy radio waves to high-energy gamma rays.

Photoelectric Effect

The release of photoelectrons from a metal surface when light of a sufficient threshold frequency shines on it.

Binding Energy ($\phi$)

The threshold amount of energy required to detach an electron from the metal surface in the photoelectric effect.

Photon

A discrete, quantized packet of light energy defined by $\text{Energy} = h\nu = \frac{hc}{\lambda}$.

Planck's Constant ($h$)

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

Emission Spectrum

The spectrum of light wavelengths emitted by an element or molecule when its excited electrons transition back to lower energy levels.

Line Spectrum

A noncontinuous emission spectrum containing distinct wavelengths characteristic of a specific element or molecule.

Bohr Model of the Atom

A model proposing that electrons travel in fixed circular orbits (stationary states) around the nucleus at quantized energy levels.

Hydrogen Energy Transitions

Quantized electronic shifts between energy levels ($n$) in hydrogen described by $\Delta E = -2.18 \times 10^{-18}\,\text{J}\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$.

Ground State

The lowest potential energy state of an atom in which all electrons occupy the lowest available energy levels.

Excited State

An unstable, higher-energy state produced when an electron absorbs energy and transitions to an orbital of higher principal quantum number.

Speed of Light Equation

The mathematical formula $c = \lambda\nu$ relating the constant speed of light ($c = 3.00 \times 10^8\,\text{m/s}$) to wavelength ($\lambda$) and frequency ($\nu$).

Photoelectron Kinetic Energy Equation

The relationship $KE = h\nu - \phi$ specifying that excess photon energy beyond the threshold binding energy ($\phi$) becomes kinetic energy of the ejected electron.

Continuous Spectrum

An unbroken spectrum displaying an uninterrupted gradient of all visible light wavelengths produced when white light passes through a prism.

Stationary States

Fixed circular orbits in the Bohr atomic model where electrons revolve around the nucleus at quantized distances without radiating energy.

Quantized Energy

Energy restricted to specific, discrete quantities or packets rather than existing across a continuous spectrum.

Principal Shell

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

Subshell

A set of atomic orbitals within a principal shell that share both the same principal quantum number ($n$) and angular momentum quantum number ($l$).

Radial Distribution Function

A representation showing the total probability of finding an electron within a thin spherical shell at a distance $r$ from the nucleus.