Chapter 6: Electronic Structure of Atoms

1. 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

2. Chapter 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)

3. Chapter 6: Electronic Structure of Atoms • Electromagnetic radiation is characterized by • wavelength (), or frequency () and • amplitude (A) l A = intensity l l

4. Chapter 6: Electronic Structure of Atoms Frequency (n) measures how many wavelengths pass a point per second: 1 s

5. Chapter 6: Electronic Structure of Atoms Electromagnetic radiation travels at the speed of light: c = 3 x 108 m s-1 Relation between wavelength, frequency, and amplitude: c =l n

6. Chapter 6: Electronic Structure of Atoms 400 nm 750 nm

7. Chapter 6: Electronic Structure of Atoms RedOrangeYellowGreenBlueUltraviolet

8. Chapter 6: Electronic Structure of Atoms What is the wavelength, in m, of radiowaves transmitted by the local radio station WHQR 91.3 MHz?

9. Chapter 6: Electronic Structure of Atoms A certain type of laser emits green light of 532 nm. What frequency does this wavelength correspond to?

10. Chapter 6: Electronic Structure of Atoms Classically, electromagnetic radiation (EMR) was thought to have only wave-like properties. Two experimental observations challenged this view: Blackbody radiation Photoelectric Effect

11. Chapter 6: Electronic Structure of Atoms Blackbody radiation • Hot objects emit light • The higher T, the higher • the emitted frequency

12. Chapter 6: Electronic Structure of Atoms Blackbody radiation prediction of classical theory = there would be NO DARKNESS Brightness “ultraviolet catastrophe” T2 T1 wavelength (l) visible region

13. Chapter 6: Electronic Structure of Atoms Blackbody radiation Max 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”

14. Chapter 6: Electronic Structure of Atoms Blackbody radiation frequency of oscillator E = h  Planck’s constant = 6.63 x 10-34 J s Energy of radiation is related to frequency, not intensity

15. Chapter 6: Electronic Structure of Atoms What is the energy of a photon of electromagnetic radiation that has a frequency of 400 kHz? = 2.65 x 10-28 J

16. Chapter 6: Electronic Structure of Atoms Photoelectric Effect Albert Einstein (1879-1955) e- e- e-

17. Chapter 6: Electronic Structure of Atoms Photoelectric Effect Albert Einstein (1879-1955) e- e- e- e- • Light of a certain minimum frequency is required to dislodge electrons from metals

18. Chapter 6: Electronic Structure of Atoms Photoelectric 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

19. Chapter 6: Electronic Structure of Atoms Relationship between Energy, Wavelength, and Frequency:

20. Chapter 6: Electronic Structure of Atoms What is the energy of a photon of light of 532 nm? = 3.74 x 10-19 J

21. Chapter 6: Electronic Structure of Atoms Electromagnetic Radiation stream of particles (photons) wave or E = h n Whether light behaves as a wave or as a stream of photons depends on themethod used to investigate it !

22. Chapter 6: Electronic Structure of Atoms Understanding light in terms of photons helped understand atomic structure many light sources produce a continuous spectrum

23. Chapter 6: Electronic Structure of Atoms Thermally excited atoms in the gas phase emit line spectra continuous spectrum (all wavelengths together: white light) line spectrum (only some wavelengths: emission will have a color)

24. Rydberg constant 1.097 x 107 m-1 positive integers (e.g. 1,2,3, etc) Chapter 6: Electronic Structure of Atoms Photograph of the H2 line spectrum (Balmer series) in the visible region (1825-1898) Johann Balmer (1825-1898)

25. Chapter 6: Electronic Structure of Atoms Niels Bohr was the first to offer an explanation for line spectra Bohr 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

26. (1885-1962) Chapter 6: Electronic Structure of Atoms Niels Bohr was the first to offer an explanation for line spectra electron orbits n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 nucleus Bohr’s Model of the Hydrogen Atom

27. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Bohr’s Model of the Hydrogen Atom Energy absorption of a photon e Ground State nucleus

28. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Bohr’s Model of the Hydrogen Atom Energy e Ground State nucleus

29. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Bohr’s Model of the Hydrogen Atom Energy “excited state” e Ground State nucleus

30. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Bohr’s Model of the Hydrogen Atom Energy e Ground State nucleus

31. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Bohr’s Model of the Hydrogen Atom Energy e Ground State emission of a photon nucleus

32. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms Which of these transitions represents an absorption process? (a) (b) (c) Energy Which of these transitions involves the largest change in energy? Which of these transitions leads to the emission of the longest wavelength photon? Ground State Does this wavelength correspond to a high or low frequency? nucleus

33. Transitions corresponding to the Balmer series Chapter 6: Electronic Structure of Atoms

34. Energy of electron in a given orbit: n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms n = Principal Quantum Number (main energy levels) h=Planck’s constant, c=speed of light, RH = Rydberg constant

35. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms For an electron moving from n = 4 to n = 2:

36. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms For an electron moving from n = 4 to n = 2: DE = - 4.09 x 10-19 J

37. n = 6 n = 5 n = 4 n = 3 n = 2 n = 1 Chapter 6: Electronic Structure of Atoms The energy of the photon emitted is: E = 4.09 x 10-19 J What wavelength (in nm) does this energy correspond to? l = 486 x 10-9 m = 486 nm

38. n=3 → n=2 n=4 → n=2 n=6 → n=2 n=5 → n=2 Chapter 6: Electronic Structure of Atoms Balmer Series l = 486 nm

39. Chapter 6: Electronic Structure of Atoms The Wave Behavior of Matter If light can behave like a stream of particles (photons)… … then (small) particles should be able to behave like waves, too For a particle of mass m, moving at a velocity v: De Broglie Wavelength e.g electrons have a wavelength (electron microscope!)

40. Chapter 6: Electronic Structure of Atoms The Uncertainty Principle Werner Heisenberg (1901-1976) and Niels Bohr

41. Chapter 6: Electronic Structure of Atoms The Uncertainty Principle It is impossible to know both the exact position and the exact momentum of a subatomic particle uncertainty in momentum, mv uncertainty in position, x

42. Chapter 6: Electronic Structure of Atoms Quantum Mechanics and Atomic Orbitals Erwin Schrödinger (1887-1961)

43. Chapter 6: Electronic Structure of Atoms Quantum 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)

44. Chapter 6: Electronic Structure of Atoms Quantum 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

45. z y x Chapter 6: Electronic Structure of Atoms Bohr’s model: n = 1 orbit electron circles around nucleus Schrödinger’s model: orbital n = 1 or electron is somewhere within that spherical region

46. Chapter 6: Electronic Structure of Atoms Bohr’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 number l : second or azimuthal quantum number ml: magnetic quantum number

47. - energy of electron in a given orbital: Chapter 6: Electronic Structure of Atoms Schrödinger’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 ….

48. - lis normally listed as a letter: Value of l: 0 1 2 3 letter: spdf Chapter 6: Electronic Structure of Atoms Schrödinger’s model: (2)l = azimuthal quantum number - takes integral values from 0 to n-1 e.g. n = 3 - ldefines the shape of an electron orbital

49. p-orbital (1 of 3) d-orbital (1 of 5) f-orbital (1 of 7) Chapter 6: Electronic Structure of Atoms Schrödinger’s model: z y x s-orbital

50. Chapter 6: Electronic Structure of Atoms Schrödinger’s model: (3) ml = magnetic quantum number - takes integral values from -lto +l, including 0 e.g. l = 2 - mldescribes the orientation of an electron orbital in space