Chapter 6 Electronic Structure of Atoms

1. 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.

2. 6.1 The Wave Nature of Light

3. Light • Much of our understanding of electronic structure of atoms comes from analysis of the light absorbed or emitted by substances • The light that we see as colors is only a very small portion of the electromagnetic spectrum

4. Radiant Energy • Electromagnetic radiation is also know as radiant energy because it carries (or radiates) energy through space • Although each type of radiant energy is unique, they all share certain fundamental characteristics… • They all behave as waves with wavelike properties

5. Waves • wavelength () = distance between corresponding points on adjacent waves • crest to crest, trough to trough • units of meters (m) or nanometers (nm) • amplitude = height of the wave

6. Waves • frequency ( ) = the # of complete wavelengths, or cycles, passing a given point per unit of time • units of s–1 or hertz (Hz) • For waves traveling at the same velocity, the longer the , the smaller the  •  and  are inversely proportional (as one increases, the other) Short  = High  Long  = Low 

7. Shared Characteristics of Radiant Energy • All radiation moves through a vacuum at the same velocity: speed of light (c) = 3.0 x 108 m/s • This common speed allows  and  to have a quantitative relationship • c = 

8. The Electromagnetic Spectrum

9. Concept Questions: • Which of the following has the highest frequency? Ultraviolet (UV) waves or Infrared (IR) waves? • Which type of radiation has the longest wavelength? Visible light (VIS) or microwaves? • Which color of light has the shortest wavelength, and thus highest frequency? violet

10. 6.2 Quantized Energy and Photons

11. While the wave model explains many aspects of the nature of light, there are several phenomena it does not explain

12. The Nature of Energy • It doesn’t explain how an object can glow when its temperature increases(blackbody radiation) or why the color of the glowing objects varies with the temperature • red-hot objects are cooler than white-hot

13. The Nature of Energy • Max Planck  physicist who explained the relationship between temperature, light intensity, & wavelengths of emitted radiation • Planck assumed energy could only be released or absorbed by atoms in discrete “chunks” called quanta (the smallest quantity of energy emitted/absorbed by radiation)

14. Quantized Energy & Quantum Theory • A single quanta has a distinct amount of energy as given in the following equation: • E = h • h = 6.63  10−34 J•s (Planck’s constant) • Since energy is emitted or absorbed in discrete chunks, energy can only be absorbed/released as a whole # multiple of Plank’s constant x frequency • h , 2h, 3h • Since energy is restricted to multiples only, it is said to be quantized (staircase analogy)

15. Photoelectric Effect • In 1905, Einstein used Planck’s quantum theory to explain the photoelectric effect. • In experiments, it was observed that light shining on a clean metal surface causes e– to be emitted • For each unique metal, light below a minimum threshold frequency resulted in NO e– being emitted

16. Photoelectric Effect • The details of this effect contradicted classical physics which says radiation acts as waves • Wave theory cannot predict why frequency is the crucial factor for electron emission(wave theory supports that intensity of light would be the main factor but even the most intense light at a low frequency will not emit e–) • Einstein explained the photoelectric effect by assuming that light is made up of photons (particles) each with an energy given by, E = h http://phet.colorado.edu/en/simulation/photoelectric

17. 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

18. Practice Question: • A photon of energy has a frequency of 4.13 x1014 Hz. What is the wavelength, in nanometers, of this photon. What color of the visible spectrum would it appear to be? • c =  •  = 3.0 x 108 m/s • 4.13 x1014 Hz •  = 7.26 x 10-7m 109 nm = 726 nm = red • 1 m

19. Practice Question: • The red light from a helium-neon laser has a wavelength of 633 nm . What is the energy of one photon? • c =  and E= h • = 633 nm 1 m = 6.33 x 10-7 m 109 nm E = hc = (6.63 x 10-34Js)(3.0 x 108 m/s)  6.33 x 10-7 m = 3.14 x10-19 J

20. 6.3 Line Spectra + Bohr Model

21. Q1: The Nature of Energy Another mystery that could not be explained by wave theory involved the emission spectra observed from energy emitted by atoms and molecules.

22. Q1: Continuous Spectra • Some sources of radiation emit a single wavelength (laser) • This radiation is monochromatic (of one color) • Most radiant energy emits several wavelengths at once (lightbulbs = white light = all colors and wavelengths reflected) • When this type of radiation is sent through a prism, it is separated into its component wavelengths (forms a continuous spectrum of the rainbow)

23. Q1: Line Spectra • Not all radiation produces a continuous spectrum of colors • When gases are placed under pressure in a tube (and electricity is applied) the gases emit different colors of light (sodium = yellow, neon = red-orange) • When this light is passed through a prism, the result is a spectrum containing only a few specific wavelengths(this is known as a line emission spectra) • Every gas has a unique line spectra often referred to as it’s “fingerprint”

24. Line Spectra

25. Q2 & 3: Bohr Model of the Atom • Niels Bohr assumed e– moved around the nucleus in distinct circular paths called orbits (aka: planetary model) • Each orbit around the nucleus has a different “n” value (known as the principle quantum number) • As “n” increases, so does the radius size of the orbit and the distance of the orbit from the nucleus

26. Q2,3,&4: Bohr Model of the Atom • Each orbit has a specific quantity of energywhich increases as the value of “n” increases • Bohr, like Planck, believed energy was quantized • n = 1 is the lowest energy level; e– in this orbit are known as ground state e– and are the most stable • When electrons are in higher energy level (n = 2 through 7) they are called excited state e–

27. Q2 & 4: Electron “Jumping” • According to Bohr, electrons can “jump” between energy levels only if the exact amount of energy needed was gained or lost by the e– (like rungs on a ladder) • e– demotion = moving from higher  lower“n” will emit radiant energy (energy released) • e– promotion = moving from lower  higher “n” will absorb radiant energy (energy required)

28. () 1 nf2 E = −RH - 1 ni2 The Rydberg Equation The energy absorbed or emitted (ΔE) from the process of electron “jumping” can be calculated by the equation: • RH = Rydberg constant = 2.18  10−18J • niand nf= initial and final energy levels of the e– • e– demotion= - ΔE • e– promotion= + ΔE

29. Explanation - Line Emission Spectra • The specific spectral lines seen when an element’s radiant energy is separated through a prism can mathematically be related to the Rydberg equation • Thus, the existence of these spectral lines is due to the quantized jumps made by e– between energy levels • Since each element has a different # of e–(in different energy levels), the energy of each “jump” will be different, resulting in unique  (and colors) for every element = unique line emission spectra!!!

30. Q5: Limitations of Bohr Model • Bohr model offers an accurate explanation for the Hydrogen line emission spectra (b/c it only has one e–), but does not as accurately apply to the spectra of other atoms • Also, his model only views the electron as a particle and ignores the wavelike properties that exist • Thus, the Bohr model was only a step towards a more comprehensive atomic model, but it did produce two significant ideas: 1) electrons can only exist in discrete energy levels 2) energy is involved in moving electrons between the energy levels

32. 6.4 The Wave Behavior of Matter

33. h mv  = Q1: The Wave Behavior of Matter • Louis de Broglie postulated that if light can behave as particles of matter, then matter should also be able to exhibit wave properties (“matter waves”) • Ex) e– moving about the nucleus as a wave would have characteristic wavelength & frequency • The  (in m) of any matter would depend on its mass (in kg) & velocity (m/s) • For matter with an ordinary mass (even just a golf ball) the  would be so tiny it would be imperceptible 1 J = 1 kg•m2 s2

34. h mv  = The de Broglie Equation Determine the wavelength of the following: • A 7000 g bowling ball rolls with a velocity of 8.0 m/s.  = 6.63 x 10-34 J•s = 1.18 x 10-35 m (7.0 kg)(8.0 m/s) b) What is the wavelength of an electron moving at 5.31 x 106 m/s? The mass of an electron is 9.11 x 10-31kg  = 6.63 x 10-34J•s = 1.37 x 10-10m (9.11 x 10-31kg)(5.31 x 106 m/s) http://www.youtube.com/watch?v=JIGI-eXK0tg

35. Proof of de Broglie Theory • A few years after his proposed theory, experimental results backed de Broglie • Electrons passed through a solid crystal and were diffracted (broken up around slits just like a beam of light) • The double-slit experiment,demonstrates that matter and energy can display characteristics of both waves and particles • This technique leads to the development of the electron scanning microscope • http://www.youtube.com/watch?v=MTuyEn-ngIQ

36. Chicken Embryo; Termite;Dust Mite; Spider

37. h 4 (x) (mv)  Q2: The Uncertainty Principle • The dual nature of matter places a fundamental limitation on how accurately both the speed and position of an object can be known • This limitation becomes important only when matter is of subatomic size • Werner Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • Therefore, it is impossible to know both the location and momentum of an electron The smaller the mass, the more uncertainty there is in its position • http://www.youtube.com/watch?v=32oUlB2BfEA

39. Bohr’s Model… incorrect • Why does the Bohr model of the atom violate the uncertainty principle? • Bohr  thought e– traveled in orbits • this cannot be true, b/c then the exact path and position of an e– would be known at all times • De Broglie’s hypothesis and Heisenberg's uncertainty principle set the stage for a new model of the atom • Recognizes the wave nature of e– and the distinct energy levels that Bohr founded to describe theprobablelocation of an e–

40. Quiz Review: 6.1 – 6.4 • List all 7 types of radiation on the EM Spectrum in order of increasing frequency. • Radio, Microwaves, IR, Visible, UV, X-rays, Gamma rays • There is a(n) ____________ relationship between wavelength and frequency. • Energy and frequency are _____________ proportional to one another, meaning as one increases, the other _____________. • The units for: • Frequency: _______________ • Wavlength: _______________ • Energy: ______________ indirect directly increases Hz = s-1 m or nm J

41. ( ) 1 nf2 - E= −RH 1 ni2 Quiz Review: 6.1 – 6.4 • Important Equationsto MEMORIZE (constants will be given) • c =  • E = h [Rydberg] • E = hc= h  • Continuous spectra vs. line spectra • Photoelectric effect – Einstein proved that waves behaved as particles • Bohr model of the atom • Energy levels/orbits, ground state vs. excited state • Useful parts of the Bohr model? • Absorbtion/Emissison of energy & electron jumping (relationship to quantized energy • Heisenberg’s Uncertainty Principle – how does Bohr’s model violate this principle?

42. 6.5 Quantum Mechanics & Atomic Orbitals

43. Quantum Mechanics • In 1926, Erwin Schrödinger developed an equation (Schrodinger’s wave equation), which incorporated both the wave and particle natures of matter • This new way of dealing with subatomic particles is known as quantum mechanics.

44. Quantum Mechanical Model • Applies Heisenberg’s uncertainty principle and distinct energy levels from Bohr model • The quantum mechanical model of the atom statistically describes a general region of space around the nucleus where an electron is likely to be found at any given instant

45. Electron Density Distribution • From Schrodinger’s wave equation, locations around the nucleus with the highest density of plotted “dots” represent the areas around the nucleus where an e– is most likely to be found

46. Quantum Numbers • Mathematically solving the wave equation gives a set of wave functions (aka: orbitals) and their corresponding energies. • Each orbital … • describes the distribution of electrondensity in space. • has a characteristic energy & shape • An orbital is described by a set of three quantum numbers.

47. Principal Quantum Number, n • Also seen in Bohr model, this quantum number describes the energy level in which the orbital resides. • n values are positive integers (starting at 1) • As n increases… • the orbital become larger • e– spend more time further from the nucleus • e– have a higher energy

48. Azimuthal Quantum Number, l • This quantum number defines the shape of the orbital • Values of lare integers ranging from 0 to n − 1. • We use alphabetical letters (s, p, d, f) to communicate the different values of land, therefore, the shapes and types of orbitals (seen in section 6.6)

49. Magnetic Quantum Number, ml • Describes the three-dimensional orientation of the orbital(how the shape is oriented in space) • Values are integers ranging from -lto 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.

50. Quantum Numbers