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Electronic Structure of Atoms electronic structure: the arrangement of electrons in an atom quantum mechanics: the physics that correctly describes atoms ? electromagnetic radiation (i.e., light) -- waves of oscillating electric (E) and magnetic (B) fields -- source is… vibrating electric charges E B Characteristics of a Wave crest amplitude A trough wavelength l frequency: the number of cycles per unit time (usually sec) -- unit is Hz, or s–1 electromagnetic spectrum: contains all of the “types” of light that vary according to frequency and wavelength 750 nm 400 nm -- visible spectrum ranges from only ~400 to 750 nm (a very narrow band of spectrum) cosmic rays gamma rays X-rays UV low energy visible low f IR microwaves radio waves large l ROYGBV small l high f high energy Albert Michelson (1879) -- first to get an accurate value for speed of light Albert Michelson (1852–1931) The speed of light in a vacuum (and in air) is constant: c = 3.00 x 108 m/s -- Equation: c=nl=fl In 1900, Max Planck assumed that energy can be absorbed or released only in certain discrete amounts, which he called quanta. Later, Albert Einstein dubbed a light “particle” that carried a quantum of energy a photon. -- Equation: Max Planck (1858–1947) E=hn=hf E = energy, in J h = Planck’s constant = 6.63 x 10–34 J-s (i.e., J/Hz) Albert Einstein (1879–1955) A radio station transmits at 95.5 MHz (FM 95.5). Calculate the wavelength of this light and the energy of one of its photons. c 3.00 x 108 m/s c=fl l = = 3.14 m 6 95.5 x 10 Hz f E = h f = 6.63 x 10–34 J/Hz (95.5 x 106 Hz) = 6.33 x 10–26 J In 1905, Einstein explained the photoelectric effect using Planck’s quantum idea. -- only light at or above a threshold freq. will cause e– to be ejected from a metal surface ROYGBV e–e– – e– e– e e– e– e– e – e– e– e– light source e– e– e– e – e– metal surface Frequency (i.e., energy) of light determines IF e– are ejected or not, and with what KE. Intensity/brightness of light determines HOW MANY e– are ejected. Einstein also expanded Planck’s idea, saying that energy exists only in quanta. Light has both wavelike and particle-like qualities, and... so does matter. ? Line Spectra Ordinary white light is dispersed by a prism into a... “continuous” spectrum. From the gas in a nearly-evacuated gas-discharge tube, we instead get a... line spectrum. H2 absorption spectrum H2 emission spectrum (if the H2 is absorbing light from an external source) (if the H2 has been energized and is emitting light) Niels Bohr took Planck’s quantum idea and applied it to the e– in atoms. -- e– could have only certain amounts of energy -- e– could be only at certain distances from nucleus planetary (Bohr) model e– found here Niels Bohr (1885–1962) N e– never found here -- Bohr assumed that the e– in his circular orbits had particular energies, given by: 1 En RH 2 n RH = Rydberg constant = 2.18 x 10–18 J n = 1, 2, 3, ... (the principal quantum number) The more/less (–) an i.e., the energy level electron’s energy is... the more/less stable the atom is. “barely” (if at all) (–) E When n is very large, En “barely” e– - - - - - - - -0- - - - - - - - stable goes to zero, which is the energy “well” – most energy an e– can have e “a bit” because…zero is larger “a bit” (–) E stable e– very stable than anything (–). (e– has very (–) E escaped completely from atom.) -- Bohr stated that e– could move from one level to another, absorbing light of a particular freq. to “jump up” and releasing light of a particular freq. to “fall down.” He: 1s12 2s1 EMITTED ENERGY LIGHT (HEAT, LIGHT, ELEC., ETC.) -- Bohr’s model (i.e., its specific equation) worked only for atoms with… a single e–. Find the wavelength, frequency, and energy of a photon of the 1 En RH 2 emission line produced when an n e– in a hydrogen atom makes the transition from n = 5 to n = 2. For n = 5… 18 1 E5 2.18 x 10 2 = –8.72 x 10–20 J 5 For n = 2… E2 = –5.45 x 10–19 J DE = 4.58 x 10–19 J = energy of photon E 4.58 x 1019 J 14 Hz E=hf f = 6.91 x 10 h 6.63 x 1034 J/Hz c 3.00 x 108 m/s c=fl l = 4.34 x 10–7 m 14 f 6.91 x 10 Hz The Wave Behavior of Matter Since light (traditionally thought of as a wave) was found to behave as both a wave and a particle, Louis de Broglie suggested that matter (traditionally thought of as particles) might also behave like both a wave and a particle. He called these… Louis de Broglie (1892–1987) matter waves. -- The wavelength of a moving sample of matter is given by: h h l p mv m = mass (kg) v = speed (m/s) A proton moving at 1200 m/s would be associated with a matter wave of how many nanometers? In the absence of further info… 1g 1 kg mp ~ 1 amu 23 6.02 x 10 amu 1000 g = 1.66 x 10–27 kg (actual p+ mass is ~1.673 x 10–27 kg) h 6.63 x 1034 J/Hz l mv (1.66 x 1027 kg) (1200 m/s) = 3.3 x 10–10 m = 0.33 nm 1 nm 9 1 x 10 m A wave is smeared out through space, i.e., its location is not precisely defined. Since matter exhibits wave characteristics, there are limits to how precisely we can define a particle’s (e.g., an e–’s) location. -- the limitation also applies to a particle’s...momentum -- Heisenberg’s uncertainty principle: It is impossible to know simultaneously BOTH the exact momentum of a particle AND its exact location in space. h Dx D(mv ) 4 D = “uncertainty in” h = Planck’s const. (It is inappropriate to imagine an e– as a solid particle moving in a well-defined orbit.) Werner Heisenberg (1901–1976) Schrodinger’s wave equation (1926) accounts for both wave and particle behaviors of e–. 2Y 2Y 2Y Y 2 2 V Y i 2 2m x y z t w/no where h-bar is the of reduced Planck’s constant (=h/2), V is the potential energy, Y iselectric the wave function) (for a non-relativistic particle mass and m charge and zero spin, -- Solutions to the wave equation yield wave functions, symbolized by Y, which have no physical meaning, but Y2 at any point in space gives the probability that you’ll find an e– at that point. Y2 is called the probability density, which gives the electron density. Erwin Schrodinger (1887–1961) -- Orbitals describe a specific distribution of electron density in space. Each orbital has a characteristic shape and energy. (“Not.”) (Well, theory says that there ARE g orbitals, but they don’t look like this.) WeThe alsolanthanides think g orbitals andcontain they look like this… and exist, actinides f orbitals.