Electronic Structure of Atoms

1. Electronic Structure of Atoms Resources • Our TB: Ch. 6 of Chemistry: The Central Science AP version (10th edition) • Powerpoint * (from pearson) and in-class work • POGIL activities: (1) Analysis of Spectral Lines and (2) Interaction of Radiation and Matter • Online resources for our TB (in particular online quiz) • Chem tours from ch. 7 of the W.W. Norton online book by Gilbert: • http://www.wwnorton.com/college/chemistry/chemistry3/ch/07/studyplan.aspx • Animations from Glencoe site: http://glencoe.mcgraw-hill.com/sites/0023654666/student_view0/chapter7/ • Extra quizzes from Glencoe http://glencoe.mcgraw-hill.com/sites/0023654666/student_view0/chapter7/ • Video lectures from chem guy http://www.kentchemistry.com/moviesfiles/chemguy/AP/ChemguyAtomicTheory.htm • Handouts and practice problems from M. Brophy’s web site

2. Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 6Electronic Structureof Atoms John D. Bookstaver St. Charles Community College St. Peters, MO  2006, Prentice Hall, Inc.

3. Waves • To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength().

4. Waves • The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

5. Electromagnetic Radiation • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. • Therefore, c = 

6. The Nature of Energy • 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.

7. The Nature of Energy • Einstein used this assumption to explain the photoelectric effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63  10−34 J-s (i.e. units for h are J•s)

8. The Nature of Energy • Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

9. For electromagnetic radiation animation and problems see: http://www.wwnorton.com/college/chemistry/gilbert2/tutorials/interface.asp?chapter=chapter_07&folder=frequency_wavelength For All Chem tours for the electrons in atoms and periodic properties topic see: http://www.wwnorton.com/college/chemistry/chemistry3/ch/07/studyplan.aspx Recommeded chem tours animations: Electromagnetic radiation Light Emission and Absorbtion Bohr Model of the Atom De Broglie Wavelngth Quantum numbers Electron configuration

10. The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

11. The Nature of Energy • One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.

12. Go To Glencoe Animation http://glencoe.com/sites/common_assets/advanced_placement/chemistry_chang9e/animations/chang_7e_esp/pem1s3_1.swf POGIL activity on Spectral Lines (To Complete)

13. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).

14. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.

15. The Nature of Energy • Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • 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

16. 1 nf2 ( ) - E = −RH 1 ni2 The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: 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.

17. Go To Glencoe and Norton Animations http://glencoe.com/sites/common_assets/advanced_placement/chemistry_chang9e/animations/chang_7e_esp/pem1s3_1.swf POGIL activity on Interaction of Radiation and Matter (To Complete) Go to Chem tour for Bohr Model of atom (and Rydberg equation) http://www.wwnorton.com/college/chemistry/chemistry3/ch/07/chemtours.aspx

18. h mv  = The Wave Nature of Matter • Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass and wavelength was

19. h 4 (x) (mv)  The 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!

20. Quantum Mechanics • Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics.

21. The Quantum Mechanical Model • Energy is quantized - It comes in chunks. • A quantum is the amount of energy needed to move from one energy level to another. • Since the energy of an atom is never “in between” there must be a quantum leap in energy. • In 1926, Erwin Schrodinger derived an equation that described the energy and position of the electrons in an atom • (this slide from: J. Hushen’s presentation on Atomic Structure at http://teachers.greenville.k12.sc.us/sites/jhushen/Pages/AP%20Chemistry.aspx)

22. Schrodinger’s Wave Equation Equation for the probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger (this slide from: J. Hushen’s presentation on Atomic Structure at http://teachers.greenville.k12.sc.us/sites/jhushen/Pages/AP%20Chemistry.aspx)

23. Quantum Mechanics • The wave equation is designated with a lower case Greek psi (). • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

24. Quantum Numbers • 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.

25. 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.

26. Azimuthal Quantum Number, l • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

27. Azimuthal Quantum Number, l

28. 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.

29. Magnetic Quantum Number, ml • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells.

30. Allowed Sets of Quantum Numbers for Electrons in Atoms Leveln 1 2 3 Sublevel l 0 0 1 0 1 2 Orbital ml 0 0 0 0 -1 1 -1 2 1 -1 -2 1 0 0 = +1/2 Spin ms = -1/2

31. s Orbitals • Value of l = 0. • Spherical in shape. • Radius of sphere increases with increasing value of n.

32. s Orbitals 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.

33. p Orbitals • Value of l = 1. • Have two lobes with a node between them.

34. d Orbitals • Value of l is 2. • Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

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

36. 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.

37. Spin Quantum Number, ms • In the 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.

38. Spin Quantum Number, ms • This led to a fourth quantum number, the spin quantum number, ms. • The spin quantum number has only 2 allowed values: +1/2 and −1/2.

39. Pauli Exclusion Principle • No two electrons in the same atom can have exactly the same energy. • For example, no two electrons in the same atom can have identical sets of quantum numbers.

40. Go To www.ptable.com IMPORTANT • Use periodic Table to help you write electron configurations of atoms (and ions) Dynamic Periodic Table and Investigate (play with) the Orbitals option (on Top Tabs) for quantum numbers, orbitals and electron configurations of various elements Go To Glencoe site for animations on electron configuration http://glencoe.mcgraw-hill.com/sites/0023654666/student_view0/chapter7/animations_center.html#

41. Electron Configurations • Distribution of all electrons in an atom • Consist of • Number denoting the energy level

42. Electron Configurations • Distribution of all electrons in an atom • Consist of • Number denoting the energy level • Letter denoting the type of orbital

43. 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.

44. Orbital Diagrams • Each box represents one orbital. • Half-arrows represent the electrons. • The direction of the arrow represents the spin of the electron.

45. Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”

46. Periodic Table • We fill orbitals in increasing order of energy. • Different blocks on the periodic table, then correspond to different types of orbitals.

47. Some Anomalies Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.

48. Some Anomalies For instance, the electron configuration for chromium is [Ar] 4s1 3d5 rather than the expected [Ar] 4s2 3d4. N.B. Copper is another anomaly.

49. Some Anomalies • This occurs because the 4s and 3d orbitals are very close in energy. • These anomalies occur in f-block atoms, as well.

50. MAGNETISM • magnetite--Fe3O4, natural magnetic oxide of iron • 1600--William Gilbert concluded the earth is also a large spherical magnet with magnetic south at the north pole (Santa's habitat). • NEVER FORGET: opposites attract & likes repel • PARAMAGNETISM AND UNPAIRED ELECTRONS • diamagnetic--not magnetic [magnetism dies]; in fact they are slightly repelled. All electrons are PAIRED. • paramagnetic--attracted to a magnetic field; lose their magnetism when removed from the magnetic field; HAS ONE OR MORE UNPAIRED ELECTRONS • ferromagnetic--retain magnetism upon introduction to, then removal from a magnetic field • All of these are explained by electron spins • Each electron has a magnetic field with N & S poles • electron spin is quantized such that, in an external magnetic field, only two orientations of the electron magnet and its spin are possible • +/- 1/2 • H is paramagnetic; He is diamagnetic, WHY? • H has one unpaired electron • He has NOunpaired electrons; all spins offset and cancel each other out • (Taken from summary notes posted on M. Brophy’s website) • ELECTRON SPIN • 1920--chemists realized that since electrons interact with a magnetic field, there must be one more concept to explain the behavior of electrons in atoms. • ms--the 4th quantum number; accounts for the reaction of electrons in a magnetic field