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. October 31Next test unit 6 and 7 together • The nature of waves • 6.9 to and 6.17 ODD 6.12 • Photoelectric Effect • Line Spectra • Bohr Model • Quantum Model • Hw for the whole chapter 6 • 21to 37 odd only and 43 • 47 to 53 odd only • 63,66,67,68,71,72,73,75

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. Long Wavelength Low Frequency Low energy Short Wavelength High Frequency High energy Waves

6. Light and Waves • All waves have a characteristic wavelength, l (lambda) and amplitude, A. • The frequency, n (nu) 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. m∙s-1 Hz (s-1) m

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

8. Modern atomic theory arose out of studies of the interaction of radiation (light) with matter. • Electromagnetic radiation moves through a vacuum with a speed of 2.99792458  108 m/s. • Electromagnetic waves have characteristic wavelengths and frequencies. • Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).

9. The Wave Nature of Light

10. Examples Calculate the frequency of light with a wavelength of 585 nm. Calculate the wavelength of light with a frequency of 1.89 x 1018 Hz.

11. 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.

12. NOVEMBER 1 • Plank – proposed quantization of energy • Einstein – proposed and explanation for the photoelectric effect. Light behave like a particle- Photon- • BOHR THEORY AND THE SPECTRA OF EXCITED ATOMS • BALMER SERIES AND LYMAN SERIES

13. Quantized Energy and Photons • Planck: energy can only be absorbed or released from atoms in certain amounts called quanta. • The relationship between energy and frequency is • where h is Planck’s constant (6.626  10-34 J·s). • To understand quantization consider walking up a ramp versus walking up stairs: • For the ramp, there is a continuous change in height whereas up stairs there is a quantized change in height.

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

15. The Photoelectric Effect and Photons • The photoelectric effect provides evidence for the particle nature of light -- “quantization”. • If light shines on the surface of a metal, there is a point at which electrons are ejected from the metal. • The electrons will only be ejected once the threshold frequency is reached (work function- energy needed for an electron to overcame the attractive forces that hold it in a metal. • Below the threshold frequency, no electrons are ejected. • Above the threshold frequency, the number of electrons ejected depend on the intensity of the light.

16. 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.

17. Einstein assumed that light traveled in energy packets called photons. • The energy of one photon:

18. Einstein • Said electromagnetic radiation is quantized in particles called photons. • Each photon has energy = hn = hc/l • Combine this with E = mc2 • You get the apparent mass of a photon. • m = h / (lc)

19. Examples • Calculate the energy of a photon of light with a frequency of 7.30 x 1015 Hz. • Calculate the energy of red light with a wavelength of 720 nm. • Calculate the energy of a mole of photons of that red light. • Calculate the wavelength of a photon with an energy value of 4.93 x 10-19 J.

20. Examples • Calculate the energy of a photon of light with a frequency of 7.30 x 1015 Hz. • 4.84 x 10-18 J • Calculate the energy of red light with a wavelength of 720 nm. • 2.76 x 10-19 J • Calculate the wavelength of a photon with an energy value of 4.93 x 10-19 J. • 403 nm (4.03 x 10-7 m)

21. The Nature of Energy Another mystery involved the emission spectra observed from energy emitted by atoms and molecules. When gases at low pressure were placed in a tube and were subjected to high voltage, light of different colors appeared

22. Line Spectra and the Bohr Model • Continuous Spectra • 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. • Note that there are no dark spots on the continuous spectrum that would correspond to different lines.

24. Line Spectra If high voltage is applied to atoms in gas phase at low pressure light is emitted from the gas. If the light is analyzed the spectrum obtained is not continuous. SPECTROSCOPE

25. Line Spectra. When the light from a discharge tube is analyzed only some bright lines appeared.

26. NOVEMBER 2 • Hydrogen Spectra • Balmer series • Lyman Series • Paschem Series

27. Bohr’s Model • Niels Bohr adopted Planck’s assumption about energy and explained the hydrogen spectrum this way: 1. Only orbits of certain radii corresponding to certain definite energies are permitted for the electron in the hydrogen atom.

28. Bohr Model • 2 An electron in a permitted orbit has a specific energy an is in an “allowed” energy state. It will not spiral into the nucleus • 3 Energy is emitted or absorbed by the electron only as the electron changes from one allowed state to other

29. Hydrogen Line Spectrum • The line spectrum for H has 4 lines in the visible region. • Johan Balmer in 1885 showed that the wavelengths of these lines fit a simple formula. Later on additional lines were found in the ultraviolet (Lyman series) and infrared (Pashem series)region. The equation was extended to a more general one that allowed the calculation of the wavelength for all lines of Hydrogen

30. 1 nf2 ( ) - E = −RH 1 ni2 Energy states of the Hydrogen Atom 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.

32. Balmer series • If n=3 the wavelength of the red light in the Hydrogen Spectrum is obtained (656 nm) • If n=4 the wavelength of the green line is calculated • If n=5 and n=6 the equation give the wavelength for the blue lines

33. Balmer series. Visible range • Electrons moving from states with n>2 to the n=2 state

34. Lyman Series • Emission lines in the ultraviolet region. • Electrons moving from states with n>1 to state=1

35. Paschem Series • In the infrared area of the spectrum. • From other energy levels to n = 1 • The largest jump, high energy, ultraviolet region.

36. Limitations of Bohr’s Model • It does offer an explanation for the line spectrum of hydrogen, but it cannot explain other atoms. • The two main contributions are that a) Electrons exist only in certain energy levels. b) If electrons move to another permitted energy level it must absorbed or emit energy as light.

37. Which is it? • Is energy a wave like light, or a particle? • Both! Concept is called the Wave -Particle duality. • What about the other way, is matter a wave? • Yes

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

39. Flame Test • The flame test is used to visually determine the identity of an unknown metal or metalloid ion based on the characteristic color the salt turns the flame of a bunsen burner. The heat of the flame converts the metal ions into atoms which become excited and emit visible light. The characteristic emission spectra can be used to differentiate between some elements.

40. Flame Test Colors • Li+                                       Deep red (crimson) • Na+                                       Yellow-orange • K+                                       Violet - lilac • Ca2+                                    Orange-red • Sr2+                                     Red • Ba2+                                    Pale Green • Cu2+                                    Green

41. Matter waves • De Broglie described the wave characteristics of material particles. • mv is the momentum • His equation is applicable to all matter, however the wavelength associated with objects of ordinary size would be so tiny that could not be observed. • Only for objects of the size of the electrons could be detected

42. 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! h 4 (x) (mv) 

43. The Uncertainty Principle • Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously. • For electrons: we cannot determine their momentum and position simultaneously. • If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then

44. 5th Solvay Conference of Electrons and Photons - 1927

45. 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.

46. 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.

47. NOVEMBER 3 • QUANTUM MECHANICS AND ATOMIC ORBITALS • ELECTRON CONFIGURATION.

48. 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.

49. 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. • As n becomes larger, the electron is further from the nucleus.

50. Azimuthal Quantum Number, l(Angular momentum quantum #)SUBSHELLS • 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.