1. Daniel L. Reger Scott R. Goode David W. Ball www.cengage.com/chemistry/reger Lecture 07 (Chapter 7) Electronic Structure

2. Core Concepts Wave nature of light Relationship between wavelength and frequency EM Spectrum Plancks quantization of energy Photoelectric effect Atomic line spectra and energy levels (Bohr) Quantum Mechanics Heisenberg’s Uncertainty Principle Quantum numbers of electrons

3. Constants, Variables, Equations λ = lambda (wavelength) υ = upsilon (speed, de Broglie) ν = nu (frequency) h = Planck’s constant (6.626 x 10 -34 J*s) R H = 2.179 x 10 -18 J Mass of electron m=9.1 x 10 -31 kg c = wave speed of light (3.0 x 10 8 m/s) For n = 1, 2,3,…∞

4. Energy and stability of the atom –Ernest Rutherford nuclear model (1911): a nucleus with mass surrounded by electrons with little mass. –Problem: according to current theory at that time, the atoms would essentially collapse as flying electrons lost energy. –How can the atom remain stable over time? + - - - - - -

5. How do electrons in atom remain stable over time? To answer this question, we need to understand 2 important aspects associated with electrons and their place within the atom Quantization of energy Wave-Particle duality

6. Waves are periodic disturbances (through matter or a physical field) that repeat at regular intervals of time and distance. Wavelength ( ) is the distance between one peak and the next. Frequency ( ) is the Number of wavelengths that pass through a fixed point in a given unit of time (e.g., 1s or Hz). Waves and Wave Properties

7. Waves are periodic disturbances (through matter or a physical field) that repeat at regular intervals of time and distance. Waves

8. Wavelength and Frequency http://www.physicsforums.com/showthread.php?t=57843 Time = 1s 1 Hz 2 Hz 4 Hz 8 Hz 16 Hz

9. Light or electromagnetic radiation consists of oscillating electric and magnetic fields. Electromagnetic Radiation

10. Electromagnetic Spectrum Light is visible portion of a much larger energy continuum…

11. All electromagnetic waves travel at the same speed in a vacuum, 3.00×10 8 m/s. The speed of a wave is the product of its frequency and wavelength, so for light: So, if either the wavelength or frequency is known, the other can be calculated. Speed of Light

12. An FM radio station broadcasts at a frequency of 100.3 MHz (1 Hz = 1 s -1 ). Calculate the wavelength of this electromagnetic radiation. Example: Electromagnetic Radiation

13. An FM radio station broadcasts at a frequency of 100.3 MHz (1 Hz = 1 s -1 ). Calculate the wavelength of this electromagnetic radiation. Example: Electromagnetic Radiation

14. At T > 0 K, matter emits EMR across EM spectrum. For visible light, different colors indicate differences in energy. In 1900, Max Planck, working with heated solids, observed color changes with temperature increases. Planck theorized that atoms of the solid oscillate with a definite frequency (ν), but atoms could have only certain energies of vibrations (i.e., they are quantized into discrete levels). He then proposed a smallest unit of energy, called a quantum, and this energy is represented by Planck’s equation: where h is Planck’s constant, 6.626×10 -34 J·s, and ν is the frequency. Quantization of Energy

15. The Photoelectric Effect Planck’s experiments described the photoelectric effect: electrons are ejected from a metal when it is exposed to light. All metals have a threshold frequency, 0, so if the frequency of light is less than the threshold, no matter how intense the light, no electrons are ejected. If the light frequency exceeds the threshold frequency, 0, electrons are ejected, and increasing the light intensity increases the number of electrons released.

16. Einstein applied Planck’s equation to the photoelectric effect, and suggested that light can behave as a stream of particles (photons) in addition to behaving as a wave. The energy of each photon is given by Planck’s equation, E = h. The minimum energy needed to free an electron is h 0. The energy of the photon (hv) required to dislodge an electron had to be equal to the energy required to separate the electron from the solid (hv 0 ), and the KE of the electron (conservation of energy). Photoelectric Effect (cont.)

17. Wave-particle duality Light has both particle and wave properties, depending on the property. Particle behavior, wave behavior no longer considered to be exclusive from each other. Dual Nature of Light

18. A spectrum is a graph of light intensity as a function of wavelength or frequency. The light emitted by heated objects is a continuous spectrum; light of all wavelengths is present. When energy in the form of heat or electric discharge is added to sample of gaseous atoms (excitation), the atoms emit some of the added energy in the form of light (releasing photons). This produces a line spectrum that contains light only at specific wavelengths and not at others (see figure on next slide), and let’s us identify specific elements based on these spectra. Spectra

19. Line Spectra of Some Elements

20. In 1890, J. R. Rydberg studied the spectrum of hydrogen, the simplest element, and determined that the wavelengths of lines of the spectrum could be calculated using the Rydberg equation: n 1 and n 2 are positive integers (n 1 < n 2 ) and R H = 1.097×10 7 m -1. At the time, Rydberg did NOT know the meaning of the whole numbers for n 1 and n 2, but determined numbers empirically. The Rydberg Equation

21. Calculate the wavelength (in nm) of the line in the hydrogen atom spectrum for which n 1 = 2 and n 2 = 3. Example: Rydberg Equation

22. Once relationship between light energy and frequency was established, the spectra suggested that electrons were allowed only in certain discrete energy levels. In 1911, Niels Bohr proposed a model for the hydrogen atom, based on its spectrum. Bohr assumed: that the electron followed a circular orbit about the nucleus; and that the angular momentum of the electron was quantized. Using these assumptions, he found that the energy of the electron was quantized, and the allowed energy levels could be calculated using the following equation: The Bohr Model of Hydrogen

23. Assume that when one electron transfers from one orbit to another, energy must be added or removed by a single photon with energy h, and this energy is exactly equal to the difference between energies of 2 allowed levels. This assumption leads directly to the Rydberg equation. Bohr Model and the Rydberg Equation

24. Hydrogen Atom Energy Diagram Hydrogen spectra have been collected using different types of EMR, resulting in different series describing excitation of hydrogen electron, and transitions between allowed levels. We now know that electrons can absorb a photon whose E is equivalent to difference between any 2 levels.

25. Do particles exhibit wave properties? 1923, French physicist Louis de Broglie showed that electrons form standing waves. Only certain discrete rotational frequencies about the nucleus of an atom were allowed. These quantized orbits correspond to discrete energy levels. De Broglie Relation (wavelength of a particle) momentum 1927, Davidson (USA), Germer (USA) and Thomson (UK) demonstrated that beam of electrons could be diffracted by crystal (wave properties). Wavelength is inversely proportional to mass

26. At room temperature, the average speed of an electron is 1.3×10 5 m/s. The mass of the electron is about 9.11×10 -31 kg. Calculate the wavelength of the electron under these conditions. Example: de Broglie Wavelength h = 6.626×10 -34 J·s

27. De Broiglie’s equation suggested that electron wave must be a standing wave (stays in a constant position) The vibration of a string is restricted to certain wavelengths because the ends of the string cannot move. Standing Waves

28. Since the de Broglie wave of an electron in a hydrogen atom must be a standing wave, its wavelengths are restricted to values of = 2  r/n, with n being an integer, and 2  r representing the circumference of a Bohr orbit, based on quantized angular momentum. If the electron were not in a standing wave, it would partially cancel itself with each successive orbit (b), until the amplitude was zero. de Broglie Waves in the H Atom

29. Erwin Schrödinger (1887-1961) developed the current model to describe an electron wave (but we are saving the gory details for P-chem!). This wave function (  ) gives the amplitude of the electron wave at any point in space.  2 gives the probability of finding the electron at any point in space, with the electron acting like a charged cloud surrounding the atom. There are many acceptable wave functions for the electron in a hydrogen (or any other) atom. The energy of each wave function can be calculated, and these are identical to the energies from the Bohr model of hydrogen. This model lets us understand properties of electrons in atoms other than hydrogen. Schrödinger Wave Equation

30. Heisenberg’s Uncertainty Principle QM allows us to make statistical projections, but won’t allow us to describe the electron in the hydrogen atom as moving in an orbit. 1927, Werner Heisenberg demonstrated that it is not possible to know simultaneously the precise position and momentum of a particle (e.g., an electron). The less mass an object (e.g., particle) has, the more uncertainty

31. The solution of the Schrödinger equation produces quantum numbers that describe the characteristics of the electron wave function. According to QM each electron in atom is described by 4 quantum numbers, ( n,, m, m s ). The quantum numbers n,, and m, describe the distribution of the electron in three dimensional space (i.e., the atomic orbital). The atomic orbitals have definite shapes and orientations. Each orbital can contain only 2 electrons, with different spin values ( the quantum number m s ). Quantum Numbers in the H Atom

32. The principal quantum number, n, provides information about the energy and the distance of the electron from the nucleus. Allowed value of n are 1, 2, 3, 4, … The larger the value of n, the greater the average distance of the electron from the nucleus. The term principal shell (or just shell) refers to all atomic orbitals that have the same value of n. The Principal Quantum Number, n

33. Principle quantum number ( n ) Provides information about the energy and the distance of the electron from the nucleus. n is a positive integer value (1, 2, 3, 4 …). Energy of electron is most dependent upon this number. Orbital size increases as n increases. Orbitals of the same quantum state n belong to the same shell (3 s and 3 p ).

34. Angular momentum quantum number ( ) Distinguishes orbitals of given n having different shapes. can have any integer value from 0 to n – 1, but cannot be equal to n. Within each n shell, there are n different kinds of orbitals with distinct shapes. Orbitals of the same state n but different state l are subshells.

35. To identify a subshell, values for both n and must be assigned, in that order. The value of is represented by a letter: 012345etc. letterspdfghetc. Thus, a 3p subshell has n = 3, = 1. A 2s subshell has n = 2, = 0. Notations for Subshells

36. Magnetic quantum number ( m ) Distinguishes orbitals of given n and but having different orientation in space. m has 2 + 1 degenerate orbitals in each subshell. Allowed values for m l range from - to +. Example: For = 1 (p subshell), m = -1, 0, +1. These are 3 different orbitals in p subshell with the same shape but different spatial orientations.

37. Atomic Orbitals http://www.chemcomp.com/journal/molorbs.htm s subshell ( =0) 1 orbital ( m = 0) p subshell ( =1) 3 orbitals ( m = -1, 0, +1) d subshell ( =2) 5 orbitals ( m = -2, -1, 0, +1, +2)

38. Allowed Combinations of n,, m can have any integer value from 0 to n – 1, but cannot be equal to n. m has 2 + 1 degenerate orbitals in each subshell.

39. Give the notation for each of the following orbitals if it is allowed. If it is not allowed, explain why. (a) n = 4, = 1, m = 0 (b) n = 2, = 2, m = -1 (c) n = 5, = 3, m = +3 Example: Quantum Numbers

40. For each of the following subshells, give the value of the n and the quantum numbers. (a) 2s (b) 3d (c) 4p Test Your Skill

41. For each of the following subshells, give the value of the n and the quantum numbers. (a) 2s (b) 3d (c) 4p Answers: (a) n = 2, = 0 (b) n = 3, = 2 (c) n = 4, = 1 Test Your Skill

42. Spin quantum number ( m s ) There are two possible orientations of the spin axis of an electron: + ½ or -½. Spin is an intrinsic property that generates a circulating electromagnetic field (i.e., electron behaves like a magnet with north and south poles). Spin is important because it plays a critical role in electron pairing in orbitals (opposite spins are paired). Pauli Exclusion Principle No two electrons in a single atom can have the same four quantum numbers; if n,, and m are the same, m s must be different such that the electrons have opposite spins.

43. Different densities of dots or colors are used to represent the probability of finding the electron in space. Visualizing Orbitals: Electron Density Diagrams

44. Visualizing Orbitals: Contour Diagrams In a contour diagram, a surface is drawn that encloses some fraction of the electron probability (usually 90%).

45. Shapes of p Orbitals p orbitals ( = 1) have two lobes of electron density on opposite sides of the nucleus.

46. Orientation of the p Orbitals There are three p orbitals in each principal shell with an n of 2 or greater, one for each value of m. They are mutually perpendicular, with one each directed along the x, y, and z axes.

47. Shapes of the d Orbitals The d orbitals have four lobes where the electron density is high. The d z 2 orbital is mathematically equivalent to the other d orbitals, in spite of its different appearance.

48. The energies of the hydrogen atom orbitals depend only on the value of the n quantum number. The s, p, d, and f orbitals in any principal shell have the same energies. Energies of Hydrogen Atomic Orbitals

49. Other One-Electron Systems The energy of a one-electron species also depends on the value of n, and is given by the equation where Z is the charge on the nucleus. This equation applies to all one-electron species (H, He +, Li 2+, etc.). Please see example problem 7.7, p. 269.

50. In multielectron atoms, the energy dependence on nuclear charge must be modified to account for interelectronic repulsions (electrons repulse each other to an extent, as they all have negative charges). The effective nuclear charge (Z eff ) is a weighted average of the nuclear charge that affects an electron in the atom, after correction for the shielding by inner electrons and interelectronic repulsions. Effective Nuclear Charge

51. Electron shielding is the result of the influence of inner electrons on the effective nuclear charge. The effective nuclear charge that affects the outer electron in a lithium atom is considerably less than the full nuclear charge in the nucleus. Effective Nuclear Charge http://crescentok.com/staff/jaskew/isr/tigerchem/element/family10.htm

52. The 2s electron penetrates the electron density of the 1s electrons more than the 2p electrons, giving it a higher effective nuclear charge and a lower energy. Energy Dependence on

53. Within any principal shell, the energy increases in the order of the quantum number: 4s < 4p < 4d < 4f. Multielectron Energy Level Diagram

54. An orbital diagram represents each orbital with a box, with orbitals in the same subshell in connected boxes; electrons are shown as arrows in the boxes, pointing up or down to indicate their spins. Two electrons in the same orbital must have opposite spins. Orbital Diagrams ↑↓

55. Why do atoms fill orbitals the way they do? Aufbau Principle Electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g. 1s before 2s). Sometimes a low energy subshell has lower energy than upper subshell of preceding shell (e.g., 4s fills before 3d). Pauli exclusion principle QM principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously (why paired electrons have different spin). Hund's rule Every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin. 2p 2s 1s Energy

56. How to Get Aufbau from Periodic Table 1 2 3 4 5 6 7 3 4 5 6 2 3 4 5 6 7 4 5 1 For n=2, can only have 2 subshells (s, p) For n=3, can only have 3 subshells (s, p, d)

57. An electron configuration lists the occupied subshells using the usual notation (1s, 2p, etc.). Each subshell is followed by a superscripted number giving the number of electrons present in that subshell. Two electrons in the 2s subshell would be 2s 2 (spoken as “two-ess-two”). Four electrons in the 3p subshell would be 3p 4 (“three-pea-four”). Electron Configuration

58. Other Elements in the Second Period N1s 2 2s 2 2p 3 O 1s 2 2s 2 2p 4 F 1s 2 2s 2 2p 5 Ne 1s 2 2s 2 2p 6 ↑↓ ↑↑↑ ↑↑ ↑

59. Electronic Configuration Seager SL, Slabaugh MR, Chemistry for Today: General, Organic and Biochemistry, 7 th Edition, 2011 Noble gas configurations can be used to write electronic configurations in an abbreviated form in which the noble gas symbol enclosed in brackets is used to represent all electrons found in the noble gas configuration.

60. The electron configurations for some atoms do not strictly follow the aufbau principle; they are anomalous. Cannot predict which ones will be anomalous. Example: Ag predicted to be [Kr] 5s 2 4d 9 ; instead, it is [Kr] 5s 1 4d 10. Anomalous Electron Configurations