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Unit 7 Electronic Structure of Atoms

CHM 1045 : General Chemistry and Qualitative Analysis. Unit 7 Electronic Structure of Atoms. Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL. Textbook Reference : Module #9. Atoms and Electromagnetic Radiation.

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Unit 7 Electronic Structure of Atoms

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  1. CHM 1045: General Chemistry and Qualitative Analysis Unit 7Electronic Structureof Atoms Dr. Jorge L. Alonso Miami-Dade College – Kendall Campus Miami, FL • Textbook Reference: • Module #9

  2. Atoms and Electromagnetic Radiation Atoms absorb and emit energy, often in the form of electromagnetic radiation (visible light, microwaves, radio & TV waves, u.v., infrared,etc) {Fireworks}

  3. The Nature of Light Energy it is colored: the Spectrum: (1) White Light is not white, Spectroscope (2) Light is electrical and magnetic (electromagnetic) VIB G.Y O R range lue reen ellow ed iolet ndigo (3) Light does not travel in truly straight lines, it travels in waves {3D-Wave}

  4. Light Energy as Waves: two important characteristics  = high short • wavelength(): the distance (m) between corresponding points on adjacent waves  frequency () or (f ): the number of waves passing a given point per unit of time (1/s = s1-) = low long For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency  Knowing  and ,you calculate the speed of light ! SPEED = DISTANCE x PER UNIT TIME Speed (c) = wavelength (λ) x frequency () m/sec = m x 1/sec

  5. Electromagnetic Radiation A form of energy characterized by waves (or pulses) of varying frequencies () and wavelengths (). {*Light Waves} {3D-Wave} {Wavelength of v. l.}

  6. Electromagnetic Radiation Einstein’s Theory of Special Relativity: Energy and mass are different forms of the same thing • Speed of Light: All electromagnetic radiation travels at the same velocity (c), 3.00  108 m/s. E = mc2 Frequency (f ) Problem: What is the wavelength of a photon of light that has a frequency of 3.8 x 109 s-1 ? = 7.89x10-2 m

  7. The Nature of Energy: Discrete vs. Continuous Digital: 0110100101001 Analog Eggs: Water: Waves: Quanta (Photon): particles

  8. Energy as a Particle(Photon, Quanta) Light Energy When light energy shines on a metal, an electron current is generated. waves particles Light is behaving as a particle (photon) that knocks-off valence electrons from the metal. {Photoelectric Effect}

  9. Energy as a Particle (Photon, Quanta) {Metals & EM Radiation} • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta (energy bundle, photon). Max Planck (1848-1947) Planck concluded that energy (E) is proportional to frequency(): where h is Planck’s constant, 6.63  10−34 J-s. For any particular frequency () there is a particular bundle of Energy (E) that exists as a discrete quantity (quanta) that is a multiple of Planck’s constant (h).  Energy from electrons comes in discrete quantities (bundles) that are whole number multiples of h.

  10. The Nature of Energy Since c = , then  Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light. Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-14 erg? {Note: Modules use erg =10-7 Joule}

  11. The Nature of Energy E = h Problem: What is the wavelength (in Å) of a ray whose energy is 6.16 x 10-21 Joules? {Note: Modules use erg =10-7 Joule}

  12. Energy as…… (1) Waves c =    (2) Particle (Photon, Quanta) • ΔE=h  (3) Matter E = mc2

  13. h mv 1 m ∝  = The Wave-Particle Duality of Matter • Electromagnetic radiation can behave as a particle or as wave phenomena {ElectonWaves} • Louis de Broglie posited thatif light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass (m) and wavelength () was:  velocity (v) (where h is Planck’s constant, 6.63  10−34 J-s, and v is velocity of light) = eq given

  14. h mv h mv  =  = The Wave Nature of Matter Problem: An electron has a mass of 9.06 x 10-25 kg and is traveling at the speed of light. Calculate its wavelength? Problem: What is the wavelength of a 70.0 kg skier traveling down a mountain at 15.0 m/s? J = Joule = kg.m2

  15. The Nature of Energy White Light’s Continuous Spectrum: VIB G.Y O R

  16. The Nature of Energy Substances both absorb and emit only certain Discrete Spectra {AtomicSpectra} {Flame Tests.Li,Na,K} {Na,B}

  17. The Bohr “Planetary” Model of the Atom (1913) • Niels Bohr adopted Planck’s assumption and explained atomic phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies, frequencies and wavelengths, because E=h=h c/λ). • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom. 2nd EL f = 5 1st EL f = 4

  18. The Bohr Model of the Atom Which series releases most energy? The larger the fall the greater the energy {ExcitedElectrons*}

  19. Atomic Spectra & Bohr Atom 1 nf2 ( ) - RH 1 ni2 The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the Rydberg formula for hydrogen(1885) Rydberg formula for hydrogen-like elements (He+, Li 2+, Be3+ etc.,) where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron. Z is the atomic number

  20. Atomic Spectra & Bohr Atom RH nf2 1 nf2 ( ) ( ) - - E = RH = RH ni2 1 ni2 Since energy and wavelength are mathematically related, the Rydberg Equation can also be expressed in terms of energy: The energy possessed by an electron at a particular energy level (En) can be expressed as:   = eq given where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron.

  21. Atomic Spectra and the Bohr Atom Problem: How much energy (J) is liberated when an electron changes from n = 4 to n = 2? What is the wavelength (m) of the light emitted?  To convert energy to wavelength, we must employ the equations:  

  22. Atomic Spectra and the Bohr Atom Notice that the wavelength calculated from the Rydberg equation matches the wavelength of the green colored line in the H spectrum.

  23. 2006 (B) Ele 1 Ele 2

  24. h 4 (x) (mv)  Heisenberg’s Uncertainty Principle • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

  25. Quantum Model of the Atom • Max Planck (energy quanta, Planck’s constant) • Albert Einstein (energy and frequency) • Niels Bohr (electrons and Spectra) • Louis de Broglie (particle-wave duality of matter) • Werner Heisenberg (electron uncertainty) • Erwin Schrödinger (probability wave function, the four quantum numbers) • Jörge L. Alônsø (diagrammatic quantum mechanical atomic model) Prof. Alonso Solvay Conference in Brussels 1911 Seated (L-R): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz, E. Warburg, J. Perrin, W. Wien, M. Curie, and H. Poincaré.Standing (L-R): R. Goldschmidt, M. Planck, H. Rubens, A. Sommerfeld, F. Lindemann, M. de Broglie, M. Knudsen, F. Hasenöhrl, G. Hostelet, E. Herzen, J.H. Jeans, E. Rutherford, H. Kamerlingh Onnes, A. Einstein, and P. Langevin.

  26. Sublevel Orbital types = s, p, d, f 2 1 Energy Levels = 1, 2, 3, etc 3dyz 3s 3pz 3px 2pz 2s 3dxy 2px 3dxz Atom Alonsos 1s 2py 3dx2y2 3dx2 3 3py Orbital cloud orientation (x, y, z, etc) 4 Electron pair spin in Orbital cloud (2e- ea)

  27. Sublevel Orbital types = s, p, d, f 2 1 Energy Levels = 1, 2, 3, etc 3dyz 3s 3pz 3px 2pz 2s 3dxy 2px 3dxz Atom Alonsos 1s 2py 3dx2y2 3dx2 3 3py Orbital cloud orientation (x, y, z, etc) 4 Electron pair spin in Orbital cloud (2e- ea)

  28. Quantum Numbers • Describe the location of electrons within atoms. • There are four quantum numbers: • Principal = describes the energy level (1,2,3,etc) • Azimuthal = energy sublevel, orbital type (s2, p6, d10, f14) • Magnetic = orbital orientation or cloud (2 electrons on each cloud) Example: three p clouds: px, py, pz • Spin = which way the electron is spinning (↑↓)

  29. Electron Configuration, Orbital Notation and Quantum Numbers Principal (n)= energy level Azimuzal () = sublevel orbital type 1s2 2s2 2p6 3s23p63d10 4s24p64d104f14 Spin (ms) = electron + or - Magnetic (ml) = orbital cloud orientation (2e- per orbital)

  30. Electron Configuration Two issues: • Arrangement of electrons within an atom 1s22s2 2p63s23p63d104s24p64d104f14 (2) Order in which electrons fill the orbitals 1s22s22p63s23p64s23d104p65s24d105p66s24f14 Aufbau Process: Using Periodic Table Sub-blocks:

  31. Historic Development of Atomic Theory Schrödinger (1926) Bohr (1913)

  32. The Schrödinger Equation • is the imaginary unit, (complex number whose square is a negative real number) • is time, • is the partial derivative with respect to t, • is the reduced Planck's constant(Planck's constant divided by 2π), • ψ(t) is the wave function, • is the Hamiltonian (a self-adjoint operator acting on the state space). i t ψ(t)

  33. Quantum Mechanics • Developed by Erwin Schrödinger, it is a mathematical model incorporating both the wave & particle nature of electrons. • The wave function is designated with a lower case Greek psi (). • The square of the wave function, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time. {QuantumAtom}

  34. The Schrödinger Equation • Solving the wave equation gives a set of wave functions , or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. ψ(t )

  35. Principal Quantum Number, n • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers ≥ 0. 2 3 1

  36. Azimuthal Quantum Number,  • This quantum number defines the shape of the orbital. • Allowed values of  are integers ranging from 0 to n − 1. • We also use letter designations:  = 0  = 1  = 3  = 2

  37. Magnetic Quantum Number, ml • Describes the three-dimensional orientation of the orbital. • Values are integers ranging from -l to l: −l ≤ ml≤ l. • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. 0 +1 0 -1

  38. Values of Quantum Numbers • Principal Quantum #: values of n are integers ≥ 0. • Azimuthal Quantum #: values of are integers ranging from 0 to n − 1. • Magnetic Quantum #: values are integers ranging from -  to  : −≤ml≤.

  39. s Orbitals (= 0) Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron. {RadialElectronDistribution}

  40. s Orbitals (= 0) • Spherical in shape. • Radius of sphere increases with increasing value of n. {1s} {2s} {3s}

  41. p Orbitals (= 1) • Have two lobes with a node between them. {www.link} {px} +1 0 {py} {pz} -1

  42. Orbital Overlap: 1s2 2s2 2p6 = + 1s 2s 2p “P” orbital electrons are repelled by the “S” orbital electrons and so spend more time further from the nucleus. “P” orbital electrons also repel from each others’ sublevels, so they run along the axes.

  43. d Orbitals (= 2) -1 2 -2 • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center. 1 0 {*Orbitals.s.p.d} {www.link}

  44. f Orbitals (= 3) 0 • There are seven f orbitals per n level. • The f orbitals have complicated names. • They have an= 3 • m = -3,-2,-1,0,+1,+2, +3 7 values of m • The f orbitals have important effects in the lanthanide and actinide elements. 1 -1 -2 2 3 -3 {www.link.f}

  45. Energies of Orbitals • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate (collapsed).

  46. Energies of Orbitals • As the number of electrons increases, though, so does the repulsion between them. • Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate. {E.L. vs FillingOrder}

  47. Electron Configuration & Periodic Table

  48. Spin Quantum Number, ms • 1920s: it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy. {e-spin}

  49. Electron Configurations • Distribution of all electrons in an atom. • Consist of • Number denoting the energy level. • Letter denoting the type of orbital. • Superscript denoting the number of electrons in those orbitals.

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