Chapter 8: Quantum-Mechanical Model of the Atom

quantum-mechanical model

A model that explains the behavior of absolutely small particles such as electrons and photons.

electromagnetic radiation

A form of energy embodied in oscil-lating electric and magnetic fields.

amplitude

The vertical height of a crest (or depth of a trough) of a wave; a measure of wave intensity.

wavelength

(λ) The distance between adjacent crests of a wave.

frequency

(v) For waves, the number of cycles (or complete wavelengths) that pass through a stationary point in one second.

electromagnetic spectrum

The range of the wavelengths of all possible electromagnetic radiation.

gamma (y) rays

(γ) The form of electromagnetic radiation with the shortest wavelength and highest energy.

X-rays

Electromagnetic radiation with wavelengths slightly longer than those of gamma rays; used to image bones and internal organs.

ultraviolet (UV) radiation

(UV) Electromagnetic radiation with slightly smaller wavelengths than visible light.

visible light

Those frequencies of electromagnetic radiation that can be detected by the human eye.

infrared (IR) radiation

(IR) Electromagnetic radiation emitted from warm objects, with wavelengths slightly larger than those of visible light.

microwaves

Electromagnetic radiation with wavelengths slightly longer than those of infrared radiation; used for radar and in microwave ovens.

radio waves

The form of electromagnetic radiation with the longest wavelengths and smallest energy.

interference

The superposition of two or more waves overlapping in space, resulting in either an increase in amplitude (constructive interference) or a decrease in amplitude (destructive interference).

constructive interference

The interaction of waves from two sources that align with overlapping crests, resulting in a wave of greater amplitude.

destructive interference

The interaction of waves from two sources that are aligned so that the crest of one overlaps the trough of the other, resulting in cancellation.

diffraction

The phenomena by which a wave emerging from an aperture spreads out to form a new wave front.

photoelectric effect

The observation that many metals emit electrons when light falls upon them.

photon (quantum)

(quantum) The smallest possible packet of electromagnetic radiation with an energy equal to hv.

emission spectrum

(quantum) The smallest possible packet of electromagnetic radiation with an energy equal to hv.

de Broglie relation

every particle of matter exhibits wave-like properties, with a wavelength inversely proportional to its momentum

complementary properties

Properties that exclude one another; that is, the more you know about one, the less you know about the other. For example, the wave nature and particle nature of the electron are complementary.

Heisenberg's uncertainty principle

The principle stating that due to the wave–particle duality, it is fundamentally impossible to precisely determine both the position and velocity of a particle at a given moment in time.

deterministic

A characteristic of the classical laws of motion, which imply that present circumstances determine future events.

indeterminacy

The principle asserting that present circumstances do not necessarily determine future evens in the quantum-mechanical realm.

orbital

A probability distribution map, based on the quantum-mechanical model of the atom, used to describe the likely position of an electron in an atom; also, an allowed energy state for an electron.

wave function

(ψ) A mathematical function that describes the wavelike nature of the electron.

quantum number

One of four interrelated numbers that determine the shape and energy of orbitals, as specified by a solution of the Schrödinger equation.

principal quantum number (n)

(n) An integer that specifies the overall size and energy of an orbital. The higher the quantum number n, the greater the average distance between the electron and the nucleus and the higher its energy.

angular momentum quantum number

(l) An integer that deter- mines the shape of an orbital.

magnetic quantum number

(m₁) An integer that specifies the orientation of an orbital.

spin quantum number (m_s)

a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle

principal level (shell)

(shell) The group of orbitals with the same value of n.

sublevel (subshell)

(or subshell) Those orbitals in the same principal level with the same value of n and l.

probability density

function whose value at any given sample in the sample space can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample

radial distribution function

A mathematical function (corresponding to a specific orbital) that represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus.

node

A point where the wave function (ψ), and therefore the probability density (ψ²) and radial distribution function, all go through zero.

phase

With regard to waves and orbitals, the phase is the sign of the amplitude of the wave, which can be positive or negative.