1. Electronic Structure of Atoms Chapter 6

2. Introduction Almost all chemistry is driven by electronic structure, the arrangement of electrons in atoms What are electrons like? Our understanding of electrons has developed greatly from quantum mechanics

3. 6.1 Wave Nature of Light If we excite an atom, light can be emitted. This nature of this light is defined by the electron structure of the atom in question –light given off by H is different from that by He or Li, etc. –Each element is unique

4. 6.1 Wave Nature of Light The light that we can see (visible light) is only a small portion of the “electromagnetic spectrum” Visible light is a type of “electromagnetic radiation” (it contains both electric and magnetic components) Other types include radio waves, x-rays, UV rays, etc. (fig. 6.4)

5. The Wave Nature of Light

6. All waves have a characteristic wavelength,, and amplitude, A. The frequency,, of a wave is the number of cycles which pass a point in one second. The speed of a wave, v, is given by its frequency multiplied by its wavelength: For light, speed = c. c =

7. c vs. vs. The longer the wavelength, the fewer cycles are seen c = x radio station KDKB-FM broadcasts at a frequency of 93.3 MHz. What is the wavelength of the radio waves?

8. Quantized Energy and Photons Classical physics says that changes occur continuously While this works on a large, classical theories fail at extremely small scales, where it is found that changes occur in discrete quantities, called quanta This is where quantum mechanics comes into play

9. Quanta We know that matter is quantized. –At a large scale, pouring water into a glass appears to proceed continuously. However, we know that we can only add water in increments of one molecule Energy is also quantized –There exists a smallest amount of energy that can be transferred as electromagnetic energy

10. Quantization of light A physicist named Max Planck proposed that electromagnetic energy is quantized, and that the smallest amount of electromagnetic energy that can be transferred is related to its frequency

11. Quantization of light E = h –h = 6.63 x 10 -34 J. s (Planck's constant) –Electromagnetic energy can be transferred in inter multiples of h. (2h, 3h,...) To understand quantization consider the notes produced by a violin (continuous) and a piano (quantized): –a violin can produce any note by placing the fingers at an appropriate spot on the bridge. –A piano can only produce notes corresponding to the keys on the keyboard.

12. Photoelectric effect If EM radiation is shined upon a clean metal surface, electrons can be emitted For any metal, there is a minimum frequency below which no electrons are emitted Above this minimum, electrons are emitted with some kinetic energy Einstein explained this by proposing the existence of photons (packets of light energy) –The Energy of one photon, E = hν.

13. Quantized Energy and Photons The Photoelectric Effect

14. Sample Calculate the energy of one photon of yellow light whose wavelength is 589 nm

15. Sample Problems A violet photon has a frequency of 7.100 x 10 14 Hz. –What is the wavelength (in nm) of the photon? –What is the wavelength in Å? – What is the energy of the photon? –What is the energy of 1 mole of these violet photons?

16. Free Response Type Question Chlorophyll a, a photosynthetic pigment found in plants, absorbs light with a wavelength of 660 nm. –Determine the frequency in Hz –Calculate the energy of a photon of light with this wavelength

17. Bohr’s Model of the Hydrogen Atom Radiation composed of only one wavelength is called monochromatic. Radiation that spans a whole array of different wavelengths is called continuous. White light can be separated into a continuous spectrum of colors. If we pass white light through a prism, we can see the “continuous spectrum” of visible light (ROYGBIV) Some materials, when energized, produce only a few distinct frequencies of light neon lamps produce a reddish-orange light sodium lamps produce a yellow-orange light These spectra are called “line spectra

18. Bohr’s Model of the Hydrogen Atom Line Spectra Shows that visible light contains many wavelengths

19. Bohr’s Model of the Hydrogen Atom Bohr’s Model Colors from excited gases arise because electrons move between energy states in the atom. Only a few wavelengths emitted from elements

20. Bohr’s Model of the Hydrogen Atom Bohr’s Model Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra. After lots of math, Bohr showed that E = (-2.18 x 10 -18 J)(1/n 2 ) Where n is the principal quantum number (i.e., n = 1, 2, 3, …. and nothing else) “ground state” = most stable (n = 1) “excited state” = less stable (n > 1) When n = ∞, E = 0

21. Bohr Model To explain line spectrum of hydrogen, Bohr proposed that electrons could jump from energy level to energy level –When energy is applied, electron jumps to a higher energy level –When electron jumps back down, energy is given off in the form of light –Since each energy level is at a precise energy, only certain amounts of energy (  E = E f – E i ) could be emitted –I.e.

22. Bohr’s Model of the Hydrogen Atom Bohr’s Model We can show that  E = (-2.18 x 10 -18 J)(1/n f 2 - 1/n i 2 ) When n i > n f, energy is emitted. When n f > n i, energy is absorbed.

23. Sample calculation (Free Response Type Question) In the Balmer series of hydrogen, one spectral line is associate with the transition of an electron from the fourth energy level (n=4) to the second energy level n=2. –Indicate whether energy is absorbed or emitted as the electron moves from n=4 to n=2. Explain (there are no calculations involved) –Determine the wavelength of the spectral line. –Indicate whether the wavelength calculated in the previous part is longer or shorter than the wavelength assoicated with an electron moving from n=5 to n=2. Explain (there are no calculations involved)

24. Wave Behavior of Matter EM radiation can behave like waves or particles Why can't matter do the same? Louis de Broglie made this very proposal –Using Einstein’s and Planck’s equations, de Broglie supposed:

25. What does this mean? In one equation de Broglie summarized the concepts of waves and particles as they apply to low mass, high speed objects As a consequence we now have: –X-Ray diffraction –Electron microscopy

26. Sample Exercise Calculate the wavelength of an electron traveling at a speed of 1.24 x 10 7 m/s. The mass of an electron is 9.11 x 10 -28 g.

27. Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine the exactly the position, direction of motion, and speed simultaneously. For electrons: we cannot determine their momentum and position simultaneously. The Uncertainty Principle

28. Quantum Mechanics and Atomic Orbitals Schrödinger proposed an equation that contains both wave and particle terms. Solving the equation leads to wave functions. The wave function gives the shape of the electronic orbital. The square of the wave function, gives the probability of finding the electron, that is, gives the electron density for the atom.

29. Quantum Mechanics and Atomic Orbitals

30. If we solve the Schrödinger equation, we get wave functions and energies for the wave functions. orbitals We call wave functions orbitals. Schrödinger’s equation requires 3 quantum numbers: Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus.

31. Orbitals and Quantum Numbers Azimuthal Quantum Number, l. Shape This quantum number depends on the value of n. The values of l begin at 0 and increase to (n - 1). We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals. Magnetic Quantum Number, m l direction This quantum number depends on l. The magnetic quantum number has integral values between -l and +l. Magnetic quantum numbers give the 3D orientation of each orbital.

32. Orbitals and Quantum Numbers

33. Sample Exercise Which element (s) has an outermost electron that could be described by the following quantum numbers (3, 1, -1, ½ )?

34. You Try Which element (s) has an outermost electron that could be described by the following quantum numbers (4, 0, 0, ½)

35. Quantum Mechanics and Atomic Orbitals Orbitals can be ranked in terms of energy to yield an Aufbau diagram. Note that the following Aufbau diagram is for a single electron system. As n increases, note that the spacing between energy levels becomes smaller.

37. Representation of Orbitals The s Orbitals All s-orbitals are spherical. As n increases, the s-orbitals get larger. As n increases, the number of nodes increase. A node is a region in space where the probability of finding an electron is zero. At a node,  2 = 0 For an s-orbital, the number of nodes is (n - 1).

38. Representation of Orbitals The s Orbitals

39. Representation of Orbitals The p Orbitals There are three p-orbitals p x, p y, and p z. (The three p-orbitals lie along the x-, y- and z- axes. The letters correspond to allowed values of m l of -1, 0, and +1.) The orbitals are dumbbell shaped. As n increases, the p-orbitals get larger. All p-orbitals have a node at the nucleus.

40. Representation of Orbitals The p Orbitals

41. Representation of Orbitals The d and f Orbitals There are 5 d- and 7 f-orbitals. Three of the d-orbitals lie in a plane bisecting the x-, y- and z- axes. Two of the d-orbitals lie in a plane aligned along the x-, y- and z- axes. Four of the d-orbitals have four lobes each. One d-orbital has two lobes and a collar.

42. Representation of Orbitals The d Orbitals

43. F Shape of f orbitals

44. Orbitals in Many Electron Atoms Orbitals of the same energy are said to be degenerate. All orbitals of a given subshell have the same energy (are degenerate) For example the three 4p orbitals are degenerate

45. Orbitals in Many Electron Atoms Energies of Orbitals

46. Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle Line spectra of many electron atoms show each line as a closely spaced pair of lines. Stern and Gerlach designed an experiment to determine why. A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected. Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction.

47. Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle

48. Orbitals in Many Electron Atoms Electron Spin and the Pauli Exclusion Principle Since electron spin is quantized, we define m s = spin quantum number =  ½. Pauli’s Exclusions Principle: Pauli’s Exclusions Principle: no two electrons can have the same set of 4 quantum numbers. Therefore, two electrons in the same orbital must have opposite spins.

49. Electron configurations tells us in which orbitals the electrons for an element are located. Three rules: electrons fill orbitals starting with lowest n and moving upwards no two electrons can fill one orbital with the same spin (Pauli) for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule). Electron Configurations

50. Details Valence electrons- the electrons in the outermost energy levels (not d). Core electrons- the inner electrons. C 1s 2 2s 2 2p 2

51. Fill from the bottom up following the arrows 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f 1s 2 2 electrons 2s 2 4 2p 6 3s 2 12 3p 6 4s 2 20 3d 10 4p 6 5s 2 38 4d 10 5p 6 6s 2 56

53. Electron Configurations and the Periodic Table

54. There is a shorthand way of writing electron configurations Write the core electrons corresponding to the filled Noble gas in square brackets. Write the valence electrons explicitly. Example, P: 1s 2 2s 2 2p 6 3s 2 3p 3 but Ne is 1s 2 2s 2 2p 6 Therefore, P: [Ne]3s 2 3p 3.

55. Exceptions Ti = [Ar] 4s 2 3d 2 V = [Ar] 4s 2 3d 3 Cr = [Ar] 4s 1 3d 5 Mn = [Ar] 4s 2 3d 5 Half filled orbitals. Scientists aren’t sure of why it happens same for Cu [Ar] 4s 1 3d 10

56. More exceptions Lanthanum La: [Xe] 6s 2 5d 1 Cerium Ce: [Xe] 6s 2 4f 1 5d 1 Promethium Pr: [Xe] 6s 2 4f 3 5d 0 Gadolinium Gd: [Xe] 6s 2 4f 7 5d 1 Lutetium Lu: [Xe] 6s 2 4f 14 5d 1

57. Diamagnetism and Paramagnetism Diamagnetism –Repelled by magnets –Occurs in elements where all electrons are paired –Usually group IIA or noble gases Paramagnetism –Attracted to magnets –Occurs in elements with one or more unpaired electrons –Most elements are paramagnetic