Key Terms

amplitude

extent of the displacement caused by a wave (for sinusoidal waves, it is one-half the difference from the peak height to the trough depth, and the intensity is proportional to the square of the amplitude)

angular momentum quantum number (l)

quantum number distinguishing the different shapes of orbitals; it is also a measure of the orbital angular momentum

atomic orbital

mathematical function that describes the behavior of an electron in an atom (also called the wavefunction), it can be used to find the probability of locating an electron in a specific region around the nucleus, as well as other dynamical variables

Aufbau principle

procedure in which the electron configuration of the elements is determined by “building” them in order of atomic numbers, adding one proton to the nucleus and one electron to the proper subshell at a time

blackbody

idealized perfect absorber of all incident electromagnetic radiation; such bodies emit electromagnetic radiation in characteristic continuous spectra called blackbody radiation

Bohr’s model of the hydrogen atom

structural model in which an electron moves around the nucleus only in circular orbits, each with a specific allowed radius; the orbiting electron does not normally emit electromagnetic radiation, but does so when changing from one orbit to another.

continuous spectrum

electromagnetic radiation given off in an unbroken series of wavelengths (e.g., white light from the sun)

core electron

electron in an atom that occupies the orbitals of the inner shells

covalent radius

one-half the distance between the nuclei of two identical atoms when they are joined by a covalent bond

d orbital

region of space with high electron density that is either four lobed or contains a dumbbell and torus shape; describes orbitals with l = 2. An electron in this orbital is called a d electron

degenerate orbitals

orbitals that have the same energy

effective nuclear charge

charge that leads to the Coulomb force exerted by the nucleus on an electron, calculated as the nuclear charge minus shielding

electromagnetic radiation

energy transmitted by waves that have an electric-field component and a magnetic-field component

electromagnetic spectrum

range of energies that electromagnetic radiation can comprise, including radio, microwaves, infrared, visible, ultraviolet, X-rays, and gamma rays; since electromagnetic radiation energy is proportional to the frequency and inversely proportional to the wavelength, the spectrum can also be specified by ranges of frequencies or wavelengths

electron affinity

energy required to add an electron to a gaseous atom to form an anion

electron configuration

electronic structure of an atom in its ground state given as a listing of the orbitals occupied by the electrons

electron density

a measure of the probability of locating an electron in a particular region of space, it is equal to the squared absolute value of the wave function ψ

excited state

state having an energy greater than the ground-state energy

f orbital

multilobed region of space with high electron density, describes orbitals with l = 3. An electron in this orbital is called an f electron

frequency (ν)

number of wave cycles (peaks or troughs) that pass a specified point in space per unit time

ground state

state in which the electrons in an atom, ion, or molecule have the lowest energy possible

Heisenberg uncertainty principle

rule stating that it is impossible to exactly determine both certain conjugate dynamical properties such as the momentum and the position of a particle at the same time. The uncertainty principle is a consequence of quantum particles exhibiting wave–particle duality

hertz (Hz)

the unit of frequency, which is the number of cycles per second, s⁻¹

Hund’s rule

every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin

intensity

property of wave-propagated energy related to the amplitude of the wave, such as brightness of light or loudness of sound

interference pattern

pattern typically consisting of alternating bright and dark fringes; it results from constructive and destructive interference of waves

ionization energy

energy required to remove an electron from a gaseous atom or ion. The associated number (e.g., second ionization energy) corresponds to the charge of the ion produced (X²⁺)

isoelectronic

group of ions or atoms that have identical electron configurations

line spectrum

electromagnetic radiation emitted at discrete wavelengths by a specific atom (or atoms) in an excited state

magnetic quantum number (m_l)

quantum number signifying the orientation of an atomic orbital around the nucleus; orbitals having different values of m_l but the same subshell value of l have the same energy (are degenerate), but this degeneracy can be removed by application of an external magnetic field

node

any point of a standing wave with zero amplitude

orbital diagram

pictorial representation of the electron configuration showing each orbital as a box and each electron as an arrow

p orbital

dumbbell-shaped region of space with high electron density, describes orbitals with l = 1. An electron in this orbital is called a p electron

Pauli exclusion principle

specifies that no two electrons in an atom can have the same value for all four quantum numbers

photon

smallest possible packet of electromagnetic radiation, a particle of light

principal quantum number (n)

quantum number specifying the shell an electron occupies in an atom

quantization

occurring only in specific discrete values, not continuous

quantum mechanics

field of study that includes quantization of energy, wave-particle duality, and the Heisenberg uncertainty principle to describe matter

quantum number

integer number having only specific allowed values and used to characterize the arrangement of electrons in an atom

s orbital

spherical region of space with high electron density, describes orbitals with l = 0. An electron in this orbital is called an s electron

shell

set of orbitals with the same principal quantum number, n

spin quantum number (m_s)

number specifying the electron spin direction, either $+\frac{1}{2}$ or $-\frac{1}{2}$

standing wave

(also, stationary wave) localized wave phenomenon characterized by discrete wavelengths determined by the boundary conditions used to generate the waves; standing waves are inherently quantized

subshell

set of orbitals in an atom with the same values of n and l

valence electrons

electrons in the outermost or valence shell (highest value of n) of a ground-state atom; determine how an element reacts

valence shell

outermost shell of electrons in a ground-state atom; for main group elements, the orbitals with the highest n level (s and p subshells) are in the valence shell, while for transition metals, the highest energy s and d subshells make up the valence shell and for inner transition elements, the highest s, d, and f subshells are included

wave

oscillation that can transport energy from one point to another in space

wave-particle duality

term used to describe the fact that elementary particles including matter exhibit properties of both particles (including localized position, momentum) and waves (including nonlocalization, wavelength, frequency)

wavefunction (ψ)

mathematical description of an atomic orbital that describes the shape of the orbital; it can be used to calculate the probability of finding the electron at any given location in the orbital, as well as dynamical variables such as the energy and the angular momentum

wavelength (λ)

distance between two consecutive peaks or troughs in a wave