Chapter 6: Electronic Structure of Atoms

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Chapter 6: Electronic Structure of Atoms. Light is a form of electromagnetic radiation (EMR) :. an oscillating charge, such as an electron, gives rise to electromagnetic radiation:. Electric Field. Magnetic Field. Chapter 6: Electronic Structure of Atoms.
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Chapter 6: Electronic Structure of AtomsLight is a form of electromagnetic radiation (EMR):
  • an oscillating charge, such as an electron, gives rise to electromagnetic radiation:
  • Electric FieldMagnetic FieldChapter 6: Electronic Structure of Atoms
  • Both the Electric and the Magnetic field propagate through
  • space
  • In vacuum, both move at the speed of light(3 x 108 m/s)
  • Chapter 6: Electronic Structure of Atoms
  • Electromagnetic radiation is characterized by
  • wavelength (), or frequency () and
  • amplitude (A)
  • lA = intensityllChapter 6: Electronic Structure of AtomsFrequency (n) measures how many wavelengths pass a point per second:1 sChapter 6: Electronic Structure of AtomsElectromagnetic radiation travels at the speed of light:c = 3 x 108 m s-1Relation between wavelength, frequency, and amplitude:c =l nChapter 6: Electronic Structure of Atoms400 nm750 nmChapter 6: Electronic Structure of AtomsRedOrangeYellowGreenBlueUltravioletChapter 6: Electronic Structure of AtomsWhat is the wavelength, in m, of radiowaves transmitted bythe local radio station WHQR 91.3 MHz?Chapter 6: Electronic Structure of AtomsA certain type of laser emits green light of 532 nm. What frequency does this wavelength correspond to?Chapter 6: Electronic Structure of AtomsClassically, electromagnetic radiation (EMR) was thought to have only wave-like properties.Two experimental observations challenged this view:Blackbody radiationPhotoelectric EffectChapter 6: Electronic Structure of AtomsBlackbody radiation
  • Hot objects emit light
  • The higher T, the higher
  • the emitted frequency
  • Chapter 6: Electronic Structure of AtomsBlackbody radiationprediction of classical theory= there would be NO DARKNESSBrightness“ultraviolet catastrophe”T2T1wavelength (l)visible regionChapter 6: Electronic Structure of AtomsBlackbody radiationMax Planck (1858 - 1947)
  • light is emitted by oscillators
  • high energy oscillators require a minimum amount of energy to be excited:
  • E = h 
  • energy is not provided by temperature in “black body”
  • Chapter 6: Electronic Structure of AtomsBlackbody radiationfrequency of oscillatorE = h Planck’s constant = 6.63 x 10-34 J sEnergy of radiation is related to frequency, not intensityChapter 6: Electronic Structure of AtomsWhat is the energy of a photon of electromagnetic radiation that has a frequency of 400 kHz?= 2.65 x 10-28 JChapter 6: Electronic Structure of AtomsPhotoelectric EffectAlbert Einstein (1879-1955)e-e-e-Chapter 6: Electronic Structure of AtomsPhotoelectric EffectAlbert Einstein (1879-1955)e-e-e-e-
  • Light of a certain minimum frequency is required to dislodge electrons from metals
  • Chapter 6: Electronic Structure of AtomsPhotoelectric Effect
  • Ability of light to dislodge electrons from metals is related to its frequency, not intensity
  • E = h 
  • This means that light comes in “units” of h
  • Intensity is related only to the number of “units”
  • The h “unit” is called a quantum of energy
  • A quantum of light (EMR) energy = photon
  • Chapter 6: Electronic Structure of AtomsRelationship between Energy, Wavelength, and Frequency:Chapter 6: Electronic Structure of AtomsWhat is the energy of a photon of light of 532 nm? = 3.74 x 10-19 JChapter 6: Electronic Structure of AtomsElectromagnetic Radiationstream of particles(photons)waveorE = h nWhether light behaves as a wave or as a stream of photons depends on themethod used to investigate it !Chapter 6: Electronic Structure of AtomsUnderstanding light in terms of photons helped understand atomic structuremany light sources produce a continuous spectrumChapter 6: Electronic Structure of AtomsThermally excited atoms in the gas phase emit line spectracontinuous spectrum (all wavelengths together: white light)line spectrum (only some wavelengths: emission will have a color)Rydberg constant1.097 x 107 m-1positive integers(e.g. 1,2,3, etc)Chapter 6: Electronic Structure of AtomsPhotograph of the H2 line spectrum (Balmer series) in the visible region(1825-1898) Johann Balmer (1825-1898)Chapter 6: Electronic Structure of AtomsNiels Bohr was the first to offer an explanation for line spectraBohr Model of the Hydrogen Atom
  • Only orbits of defined energy and radii are permitted in the hydrogen atom
  • An electron in a permitted orbit has a specific energy and will not radiate energy and will not spiral into the nucleus
  • Energy is absorbed or emitted by the electron as the electron moves from one allowed orbit into another. Energy is absorbed or emitted as a photon of E = hn
  • (1885-1962)Chapter 6: Electronic Structure of AtomsNiels Bohr was the first to offer an explanation for line spectraelectron orbits n = 1n = 2n = 3n = 4n = 5n = 6nucleusBohr’s Model of the Hydrogen Atomn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsBohr’s Model of the Hydrogen AtomEnergyabsorption of a photoneGround Statenucleusn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsBohr’s Model of the Hydrogen AtomEnergyeGround Statenucleusn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsBohr’s Model of the Hydrogen AtomEnergy“excited state”eGround Statenucleusn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsBohr’s Model of the Hydrogen AtomEnergyeGround Statenucleusn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsBohr’s Model of the Hydrogen AtomEnergyeGround Stateemission of a photonnucleusn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsWhich of these transitions representsan absorption process? (a)(b)(c)EnergyWhich of these transitions involves thelargest change in energy? Which of these transitions leads to theemission of the longest wavelength photon? Ground StateDoes this wavelength correspond to a high or low frequency? nucleusTransitions corresponding tothe Balmer seriesChapter 6: Electronic Structure of AtomsEnergy of electron in a given orbit:n = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of Atomsn = Principal Quantum Number (main energy levels)h=Planck’s constant, c=speed of light, RH = Rydberg constantn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsFor an electron moving from n = 4 to n = 2:n = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsFor an electron moving from n = 4 to n = 2:DE = - 4.09 x 10-19 Jn = 6n = 5n = 4n = 3n = 2n = 1Chapter 6: Electronic Structure of AtomsThe energy of the photon emitted is:E = 4.09 x 10-19 JWhat wavelength (in nm) does this energy correspond to?l = 486 x 10-9 m = 486 nmn=3 → n=2n=4 → n=2n=6 → n=2n=5 → n=2Chapter 6: Electronic Structure of AtomsBalmer Seriesl = 486 nmChapter 6: Electronic Structure of AtomsThe Wave Behavior of Matter If light can behave like a stream of particles (photons)…… then (small) particles should be able to behave like waves, tooFor a particle of mass m, moving at a velocity v:De Broglie Wavelengthe.g electrons have a wavelength (electron microscope!)Chapter 6: Electronic Structure of AtomsThe Uncertainty PrincipleWerner Heisenberg (1901-1976)and Niels BohrChapter 6: Electronic Structure of AtomsThe Uncertainty PrincipleIt is impossible to know both the exact position and the exact momentum of a subatomic particleuncertainty in momentum, mvuncertainty in position, xChapter 6: Electronic Structure of AtomsQuantum Mechanics and Atomic OrbitalsErwin Schrödinger (1887-1961)Chapter 6: Electronic Structure of AtomsQuantum Mechanics and Atomic Orbitals
  • Schrödinger proposed wave mechanical model of the atom
  • Electrons are described by a wave function, ψ
  • The square of the wave function, ψ2, provides information on
  • the location of an electron (probability density or electron density)
  • Chapter 6: Electronic Structure of AtomsQuantum Mechanics and Atomic Orbitals
  • the denser the stippling, the
  • higher the probability of finding
  • the electron
  • shape of electron density
  • regions depends on energy of
  • electron
  • zyxChapter 6: Electronic Structure of AtomsBohr’s model:n = 1orbitelectron circles around nucleusSchrödinger’s model:orbitaln = 1or electron is somewherewithin that spherical regionChapter 6: Electronic Structure of AtomsBohr’s model:
  • requires only a single quantum number (n) to describe an orbit
  • Schrödinger’s model:
  • requires three quantum numbers (n, l, and m) to describe an orbital
  • n: principal quantum numberl : second or azimuthal quantum numberml: magnetic quantum number- energy of electron in a given orbital:Chapter 6: Electronic Structure of AtomsSchrödinger’s model:(1) n = principal quantum number (analogous to Bohr model)- the higher n, the higher the energy of the electron- is always a positive integer: 1, 2, 3, 4 ….- lis normally listed as a letter:Value of l: 0 1 2 3letter: spdfChapter 6: Electronic Structure of AtomsSchrödinger’s model:(2)l = azimuthal quantum number- takes integral values from 0 to n-1e.g.n = 3- ldefines the shape of an electron orbitalp-orbital(1 of 3)d-orbital(1 of 5)f-orbital(1 of 7)Chapter 6: Electronic Structure of AtomsSchrödinger’s model:zyxs-orbitalChapter 6: Electronic Structure of AtomsSchrödinger’s model:(3) ml = magnetic quantum number- takes integral values from -lto +l, including 0e.g.l = 2- mldescribes the orientation of an electron orbital in spaceChapter 6: Electronic Structure of AtomsShells:
  • are sets of orbitals with the same quantum number, n
  • a shell of quantum number n has n subshells
  • Subshells:
  • are orbitals of one type within the same shell
  • total number of orbitals in a shell is n2
  • n=3 shell4f subshellChapter 6: Electronic Structure of Atoms3n =124l =00, 10, 1, 20, 1, 2, 31s2s, 2p3s, 3p, 3d4s, 4p, 4d, 4fml =00, -1,0,10; -1,0,1; -2,-1,0,1,20; -1,0,1; -2,-1,0,1,2; -3,-2,-1,0,1,2,3# orbitalsin subshell1133513517Total # of orbitalsin shell14916Chapter 6: Electronic Structure of Atoms3s-room3p-room3deluxe-room3rd floor2s-room2promotion-room2nd floorstandard-room1st floorChapter 6: Electronic Structure of AtomsOrbital energy levelsin the Hydrogen AtomChapter 6: Electronic Structure of AtomsWhat is the designation for the n=3, l=2 subshell ?How many orbitals are in this subshell ?What are the possible values for ml for each of these orbitals ?Chapter 6: Electronic Structure of AtomsWhich of the following combinations of quantum numbersis possible?n=1, l=1, ml= -1n=3, l=0, ml= -1n=3, l=2, ml= 1n=2, l=1, ml= -2Chapter 6: Electronic Structure of AtomsRepresentation of Orbitals1s2s3sChapter 6: Electronic Structure of AtomsRepresentation of Orbitals2p orbitalsChapter 6: Electronic Structure of AtomsRepresentation of Orbitalsall three p orbitalsChapter 6: Electronic Structure of AtomsRepresentation of Orbitals3d orbitalsChapter 6: Electronic Structure of AtomsWhich combination of quantum numbers is possible for theorbital shown below?(a) n=1, l=0, ml= 0(c) n=3, l=3, ml= -2(d) n=3, l=2, ml= -1(b) n=2, l=-1, ml= 1Chapter 6: Electronic Structure of AtomsThere is a fourth quantum number that characterizes electrons:spin magnetic quantum number, msms can only take two values, +1/2 or -1/2Chapter 6: Electronic Structure of AtomsWolfgang Pauli (1900-1958)A. Einstein & W. PauliChapter 6: Electronic Structure of AtomsPauli’s Exclusion Principle:No two electrons in an atom can have the same set of 4 quantum numbers, n, l, ml, and msFor a given orbital, e.g. 2s, n, l, ml are fixed: n=2, l=0, ml =0=> an orbital can only contain two electron if they differ in msChapter 6: Electronic Structure of AtomsA maximum of 2 electron can occupy one orbital, IF these two electrons have opposite spin:n=2, l=0, ml =0, ms = +1/2n=2, l=0, ml =0, ms = -1/22s2parrows pointing up/down indicate electron spinChapter 6: Electronic Structure of AtomsEnergy levels in the hydrogen atom:all subshells of a given shellhave the same energyChapter 6: Electronic Structure of AtomsEnergy levels in many-electron atoms:
  • In many-electron atoms, the energy of an orbital increases with l, for a given n
  • In many-electron atoms, the lower energy orbitals get filled first
  • orbitals with the same energy are said to be degenerate
  • Chapter 6: Electronic Structure of AtomsElectron Configurations:Line Notation:1H1s12He1s21s22s13Li1s22s24Be1s22s22p26C1s22s22p37N10Ne1s22s22p61s22s22p63s111NaChapter 6: Electronic Structure of AtomsElectron Configurations:Hund’s Rule:For degenerate orbitals, the energy is minimized when the number of electrons with the same spin is maximized=> degenerate orbitals (p, d, etc)get filled with one electron each first (same spin).1s22s22p37NChapter 6: Electronic Structure of Atomsthe Aufbau Principle helps you to remember the order in which orbitals get filled:1s2s 2p3s 3p 3d4s 4p 4d 4f5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f Chapter 6: Electronic Structure of AtomsLine notation1s22s22p63s23p214Si[Ne]3s23p2Condensed line notationorbital diagram(no energy info)3d2p1“coreelectrons”s“valence (outer shell) electrons”Chapter 6: Electronic Structure of AtomsLine notation1s22s22p63s23p214Si[Ne]3s23p2Condensed line notationorbital diagram(no energy info)3d2p1sValence electrons take part in bondingChapter 6: Electronic Structure of AtomsWhat is the electronic structure of Cl?3s23p5[Ne]17Cl :valence electrons (7)3d2p1coreelectrons = electron configurationof the preceding noble gassvalence electrons (2)coreelectrons = electron configurationof the preceding noble gasChapter 6: Electronic Structure of AtomsWhat is the electronic structure of Ca?[Ar]4s220Cl :(4s orbital is filled before 3d !)4f3d2p1scoreelectrons = electron configurationof the preceding noble gasChapter 6: Electronic Structure of AtomsWhat is the electronic structure of Br?[Ar]3d104s24p535Br :(4s orbital is filled before 3d !)valence electrons (7)4f3For main group elements,electrons in a filled d-shell(or f-shell) are not valenceelectronsd2p1sChapter 6: Electronic Structure of AtomsDoes it matter in which order the electron configuration is written ?1s22s22p63s23p63d104s24p5ordered by orbital number35Br :or:1s22s22p63s23p64s23d104p5ordered by energy4f3d2p1NO, both are correct!sChapter 6: Electronic Structure of AtomsWhat is the electron configuration of vanadium (V)?[Ar]3d34s223V:(4s orbital is filled before 3d !)4f3d2valence electrons (5)p1coreelectrons = electron configurationof the preceding noble gass[Ar]3d44s2is less stable than [Ar]3d54s1Chapter 6: Electronic Structure of AtomsWhat is the electron configuration of chromium (Cr)?[Ar]3d54s124Cr:4f3d2p1sA half-filled or completely filled d-shell is a preferred configuration1s2p2s3p3d3s4p4s4fChapter 6: Electronic Structure of AtomsChapter 6: Electronic Structure of AtomsWhat is the electronic structure of the Ca ion?[Ar]4s220Ca :[Ar]20Ca2+ :4f3d2p1sChapter 6: Electronic Structure of Atoms
  • Metals tend to lose electrons to form cations
  • Nonmetals tend to gain electrons to form anions
  • Atoms tend to gain or lose the number of electrons
  • needed to achieve the electron configuration of the closest noble gasChapter 6: Electronic Structure of AtomsWhat is the electronic structure of the ion formed by Se?[Ar]3d104s24p434Se :[Ar]3d104s24p6= [Kr]34Se2- :4f3d2p1sChapter 6: Electronic Structure of AtomsWhat is the electronic structure of the ion formed by Br?[Ar]3d104s24p535Br :[Ar]3d104s24p6= [Kr]35Br- :4f3d2p1sChapter 6: Electronic Structure of AtomsWhat is the electronic structure of the ion formed by Rb?[Kr]5s137Rb :[Kr]37Rb+ :54f3d2p1shave the same electron configuration:37Rb+,35Br-,34Se2-, and 36KrChapter 6: Electronic Structure of Atoms37Rb+ :[Ar]3d104s24p6= [Kr]35Br- :[Ar]3d104s24p6= [Kr]34Se2- :[Ar]3d104s24p6= [Kr]they are isoelectronica.b.c.d.Chapter 6: Electronic Structure of AtomsWhich of the four orbital diagrams written below for nitrogen violates the Pauli Exclusion Principle?violates Hund’s rule(all spins must point in the same direction)violates Hund’s rule(degenerate orbitals get one electron each, first)doesn’t violate anythingviolates Pauli’s Exclusion Principlethere are two same spin electrons in one orbital, i.e. all 4 quantum numbers are the same – which is impossible1s2s2pChapter 6: Electronic Structure of AtomsWhat is the total number of orbitals in the fourth shell (n=4) ?a. 16 b. 12 c. 4 d. 3what is the total number of different s,p, d and f orbitals?n=4l = 0 1 2 3s p d f0-1,0,1-3,-2,-1,0,1,2,3ml = -2,-1,0,1,2one s + three p + five d + 7 f orbitals=16 orbitals(n2)Chapter 6: Electronic Structure of AtomsWhat is the number of subshells in the third shell (n=3) ?a. 18 b. 9 c. 3 d. 1How many different types of orbitals are there?n=3l = 0 1 2s p dChapter 6: Electronic Structure of AtomsWhat is the electron configuration of the sodium cation, Na+ ? a. 1s22s22p63s1 b. 1s22s22p6 c. 1s22s22p63s2 d. 1s22s22p711Na+= 11 electrons -1 = 10 electrons1s22s22p6
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