Chapter 7

• the distance from crest to crest or trough to trough on a wave • c=λv

• the number of crests of a wave that pass a stationary point of reference per second • cycles per second • c=λv • c=spped of light=3x108

• when electromagnetic properties of radiant energy pass through air, it interacts with fewer atoms than thru solids or liquids • more interactions btwn the oscillating waves and the electrons within the atoms and molecules in solids and liquids slow the waves and bend their paths • shorter wavelengths bend more than long ones which is why violet is at the bottom of rainbows

• quantum theory: a model based on the idea that energy is absorbed + emitted in discrete quantities of energy(quanta) • the smallest discrete quantity of a particular form of energy • Planck proposed that light and all other forms of electromagnetic radiation have not only wavelike properties, but also particle-like properties on the atomic level. • Light from an object made of large, but discrete #s of atoms or molecules must be quantized • having values restricted to whole# multiples of a specific base value • steps are quantized while a ramp is continuous • A quantum of light(EM radiation) is called a photon

• the phenomenon of light striking a metal surface and producing an electric current(a flow of e-) • electrons are emitted from metals when they are illuminated by and absorb electromagnetic radiation

• the minimum frequency of light required to produce the photoelectric effect. • radiation at frequencies less than the threshold value produces NO photoelectrons aka if incoming light has v<v>0 </v><ul> <li>even a dim source of radiant energy produces at least a few phtoelectrons when the frequencies it emits are equal to or greater than v0 </li></ul> </li> </ul> </v> * Einstein proposed the threshold frequency of the minimum quantum of absorbed energy needed to remove a single electron from the surface of

• the amount of energy needed to remove an electron from the surface of a metal • 𝛟 = hv0 • If a photoelectric material is illuminated with radiation frequencies above threshold frequency(v>v0), any energy in excess of 𝛟 is imparted to each ejected e- as KE • extra energy = KE of emitted electrons • KEelectron=hv-hv0=hv-𝛟 • Ephoton=𝛟+KEelectron • the higher the frequency is above the threshold, the higher the KE and hence the velocity of ejected e-

• thebehavior of an objectthat exhibits the properties of both a wave and a particle

• Balmer determined lines corresponding to the visible emission spectrum of hydrogen fit the simple equation: • λ = 364.5 nm(m2/m2-n2) • n is 2 and m is whole# >2

• revised Balmer’s eqn(made a more general form) • 1/λ = 1.097x10-2nm-1 • n1 is a postive fixed whole number • n2 is a whole number equal to n1+1, n2+2….

• a theoretical model for the hydrogen atom that assumed its one electron travels around the nucleus in a concentric orbit. Electrons can only exist in these discrete orbits. Each orbit represents an allowed energy level and is designated by the value of n as shown in • E = 2.178 x 10-18J(1/n2) • in the bohr an electron in the orbit closest to the nucles(n=1) has the lowest energy • lines in the absorption and emission spectra represent electrons moving btwn energy levels(orbits)

• ground state: when the e- in a hydrogen atom is in the lowest (n=1) energy level • most stable • excited state: if the electron in a hydrogen atom is above n=1 energy level • hydrogen atom’s e- can move from ground to excited state(up energy level) it absorbs a quantity of energy(deltaE) that exactly matches the energy difference btwn the two excited states • electron transition: any change in e- energy that occurs by absorption or emission of energy • movement of an e- btwn energy levels

• Light is a wave that has particle properties and an electron is a particle which must have wave properties • this would mean electrons moving in atoms should have a wavelength • De Brolgie wavelength: λ = h/mv • m is momentum, a particle property • λ is wavelength, a wave property • λ = h/mu • m is mass in kg • u is velocity in m/s • not restricted to electrons

• classical mechanics(Newton) • good for large objects • not good for atoms, electrons, etc • the issue: chemistry occurs at the atomic level • solution: Quantum mechanics: combines both wave and particle aspects of matter into a unified theory

• a location in a standing wave that experiences no displacement • In the context of orbitals, nodes are locations at which electron density goes to zero

• a wave confined to a given space, with a wavelength (λ) related to the length L of the space by L 5 n(λ/2), where n is a whole number.

• the wave associated with any particle

• Blackbody radiation(heated objects emit EM radiation): classical theory does not match observations • explanation: electromagnetic radiation has particle-like properties in addition to wavelike properties

• the principle that we cannot determine both the position and the momentum of an e- in an atom at the same time • since we can’t know both position and momemntum of an e- in a hydrogen atom, the e- cannot be moving in circular orbits as implied by Bohr’s og model. • Heisenberg uncertainty principle limits us to knowing only the probability of finding an electron at a particular location in an atom • (∆x)(∆mv) ≥ h/4π • ∆x = uncertainty in position • ∆mv = uncertainty in momentum

a mathematical description of the wavelike behavior of particles on the atomic level

• a description of how the e- matter wave varies with location and time around the nucles of a hydrogen atom • wave function(𝛙): a solution the the Schrodinger wave eqn • Mathematical expressions that descrive how the matter wave of an e- in an atom varies both with time and with the location of the e- in the aotm • wave functions define energy levels in H atoms • 𝛙 2 defines an orbital • ​aka probability of finding an e-

• a region around the nucleus of an atom where the probability of finding an e- is high; each orbital is defined by 𝛙 2 and identified by a unique combination of 3 quantum #s

• a number that specifies the energy, the probable location or orientation of an orbital, or the spin of an electron within an orbital(ALL quantum numbers are integers) • principle quantum number(n): a positive integer describing the relative size and energy of an atomic orbital or group of orbitals in an atom • same as Bohr’s n • orbitals with same n are in same shell • as n increases, orbital size increases and e- are further from nucleus and, in the H atom, represent higher energy levels • generally, this is also true in multielectron atoms

• an integer having any value from 0 to n-1 that defines the shape of an orbital • orbitals with same n and l are in same subshell and have equal energy levels • l=0 → s • l=1 → p • l=2 → d • l=3 → f