Modern Atomic Theory Chapter 10

1. Modern Atomic TheoryChapter 10

2. Electromagnetic Radiation • Classical physics says matter made up of particles, energy travels in waves • Electromagnetic Radiation is radiant energy, both visible and invisible • Electromagnetic radiation travels in waves • All waves are characterized by their velocity, wavelength, amplitude, and the number of waves that pass a point in a given time

3. Figure 10.1 (a): A light wave

4. Electromagnetic Waves • velocity = c = speed of light • 2.997925 x 108 m/s • all types of light energy travel at the same speed • amplitude = A = measure of the intensity of the wave, “brightness” • wavelength =  = distance between two consecutive peaks or troughs in a wave • generally measured in nanometers (1 nm = 10-9 m) • same distance for troughs • frequency = = the number of waves that pass a point in space in one second • generally measured in Hertz (Hz), • 1 Hz = 1 wave/sec = 1 sec-1 • c =  x 

5. Figure 10.2: The different wavelengths of electromagnetic radiation

6. Planck’s Revelation • Showed that light energy could be thought of as particles for certain applications • Stated that light came in particles called quanta or photons • Particles of light have fixed amounts of energy • Basis of quantum theory • The energy of the photon is directly proportional to the frequency of light • Higher frequency = More energy in photons

7. Figure 10.3: Electromagnetic radiation

8. Problems with Rutherford’s Nuclear Model of the Atom • Electrons are moving charged particles • Moving charged particles give off energy • Therefore the atom should constantly be giving off energy • And the electrons should crash into the nucleus and the atom collapse!!

9. Atomic Spectra • Atoms which have gained extra energy release that energy in the form of light • The light atoms give off or gained is of very specific wavelengths called a line spectrum • light given off = emission spectrum • light energy gained = absorption spectrum • extends to all regions of the electromagnetic spectrum • Each element has its own line spectrum which can be used to identify it

10. Figure 10.5: Absorption and Emission Processes Absorption Emission

11. Figure 10.6: When an excited H atom returns to a lower energy level, it emits a photon that contains the energy released by the atom

12. Atomic Spectra • The line spectrum must be related to energy transitions in the atom. • Absorption = atom gaining energy • Emission = atom releasing energy • Since all samples of an element give the exact same pattern of lines, every atom of that element must have only certain, identical energy states • The atom is quantized • If the atom could have all possible energies, then the result would be a continuous spectrum instead of lines

13. Figure 10.7: When excited hydrogen atoms return to lower energy states, they emit photons of certain energies, and thus certain colors

14. Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

15. Bohr’s Model • Explained spectra of hydrogen • Energy of atom is related to the distance electron is from the nucleus • Energy of the atom is quantized • atom can only have certain specific energy states called quantum levels or energy levels • when atom gains energy, electron “moves” to a higher quantum level • when atom loses energy, electron “moves” to a lower energy level • lines in spectrum correspond to the difference in energy between levels

16. Figure 10.10: (a) Continuous energy levels. (b) Discrete (quantized) energy levels.

17. Figure 10.11: The difference between continuous and quantized energy levels

18. Bohr’s Model • Atoms have a minimum energy called the ground state • therefore they do not crash into the nucleus • The ground state of hydrogen corresponds to having its one electron in an energy level that is closest to the nucleus • Energy levels higher than the ground state are called excited states • the farther the energy level is from the nucleus, the higher its energy • To put an electron in an excited state requires the addition of energy to the atom; bringing the electron back to the ground state releases energy in the form of light

19. Figure 10.13: The Bohr model of the hydrogen atom

20. Bohr’s Model • Distances between energy levels decreases as the energy increases • light given off in a transition from the second energy level to the first has a higher energy than light given off in a transition from the third to the second, etc. • Electrons “orbit” the nucleus much like planets orbiting the sun • 1st energy level can hold 2e-1, the 2nd 8e-1, the 3rd 18e-1, etc. • farther from nucleus = more space = less repulsion • The highest energy occupied ground state orbit is called the valence shell

21. Figure 10.9: Each photon emitted by an excited hydrogen atom corresponds to a particular energy change in the hydrogen atom

22. Problems with the Bohr Model • Only explains hydrogen atom spectrum • and other 1 electron systems • Neglects interactions between electrons • Assumes circular or elliptical orbits for electrons - which is not true

23. Wave Mechanical Model of the Atom • Experiments later showed that electrons could be treated as waves • just as light energy could be treated as particles • de Broglie • The quantum mechanical model treats electrons as waves and uses wave mathematics to calculate probability densities of finding the electron in a particular region in the atom • Schrödinger Wave Equation • can only be solved for simple systems, but approximated for others

24. Figure 10.15: The probability map, or orbital, that describes the hydrogen electron in its lowest possible energy state

25. Orbitals • Solutions to the wave equation give regions in space of high probability for finding the electron - these are called orbitals • usually use 90% probability to set the limit • three-dimensional • Orbitals are defined by three integer terms that are added to the wave equation to quantize it - these are called the quantum numbers • Each electron also has a fourth quantum number to represent the direction of spin

26. Figure 10.16: The hydrogen 1s orbital

27. Orbitals and Energy Levels • Principal energy levels identify how much energy the electrons in the orbital have • n • higher values mean orbital has higher energy • higher values mean orbital has farther average distance from the nucleus • Each principal energy level contains one or more sublevels • there are n sublevels in each principal energy level • each type of sublevel has a different shape and energy • s < p < d < f • Each sublevel contains one or more orbitals • s = 1 orbital, p = 3, d = 5, f = 7

28. Figure 10.17: The first four principal energy levels in the hydrogen atom

29. Figure 10.18: Principal levels can be divided into sublevels

30. Figure 10.19: Principal level 2 shown divided into the 2s and 2p sublevels

31. Figure 10.20: The relative sizes of the 1s and 2s orbitals of hydrogen

32. Figure 10.21: The three 2p orbitals: (a) 2px, (b) 2pz, (c) 2py.

33. Figure 10.22: A diagram of principal energy levels 1 and 2 showing the shapes of orbitals that compose the sublevels

34. Figure 10.23: The relative sizes of the spherical 1s, 2s, and 3s orbitals of hydrogen

35. Figure 10.24: The shapes and labels of the five 3d orbitals

36. Pauli Exclusion Principle • No orbital may have more than 2 electrons • Electrons in the same orbital must have opposite spins • s sublevel holds 2 electrons • p sublevel holds 6 electrons • d sublevel holds 10 electrons • f sublevel holds 14 electrons

37. Orbitals, Sublevels & Electrons • for a many electron atom, build-up the energy levels, filling each orbital in succession by energy • ground state • 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p • degenerate orbitals are orbitals with the same energy • each p sublevel has 3 degenerate p orbitals • each d sublevel has 5 degenerate d orbitals • each f sublevel has 7 degenerate f orbitals

38. Figure 10.28: A box diagram showing the order in which orbitals fill to produce the atoms in the periodic table

39. Hund’s Rule • for a set of degenerate orbitals, half fill each orbital first before pairing • highest energy level called the valence shell • electrons in the valence shell called valence electrons • electrons not in the valence shell are called core electrons • often use symbol of previous noble gas to represent core electrons 1s22s22p6= [Ne]

40. Electron Configuration • Elements in the same column on the Periodic Table have • Similar chemical and physical properties • Similar valence shell electron configurations • Same numbers of valence electrons • Same orbital types • Different energy levels

41. s1 s2 p1 p2 p3 p4 p5 s2 1 2 3 4 5 6 7 p6 d1 d2d3 d4 d5 d6 d7 d8 d9 d10 f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14

42. Figure 10.25: The electron configurations in the sublevel last occupied for the first eighteen elements

43. The Modern Periodic Table • Columns are called Groups or Families • Rows are called Periods • Each period shows the pattern of properties repeated in the next period • Main Groups = Representative Elements • Transition Elements • Bottom rows = Lanthanides and Actinides • really belong in Period 6 & 7

44. Figure 10.26: Partial electron configurations for the elements potassium through krypton

45. Figure 10.27: The orbitals being filled for elements in various parts of the periodic table

46. Metallic Character • Metalloids • Also known as semi-metals • Show some metal and some nonmetal properties • Nonmetals • brittle in solid state • dull • electrical and thermal insulators • most oxides are acidic and molecular • form anions and polyatomic anions • gain electrons in reactions - reduced • Metals • malleable & ductile • shiny, lustrous • conduct heat and electricity • most oxides basic and ionic • form cations in solution • lose electrons in reactions - oxidized

47. Figure 10.31: The classification of elements as metals, nonmetals, and metalloids

48. Metallic Character • Metals are found on the left of the table, nonmetals on the right, and metalloids in between • Most metallic element always to the left of the Period, least metallic to the right, and 1 or 2 metalloids are in the middle • Most metallic element always at the bottom of a column, least metallic on the top, and 1 or 2 metalloids are in the middle of columns 4A, 5A, and 6A

49. Reactivity • Reactivity of metals increases to the left on the Period and down in the column • follows ease of losing an electron • Reactivity of nonmetals (excluding the noble gases) increases to the right on the Period and up in the column

50. Trend in Ionization Energy • Minimum energy needed to remove a valence electron from an atom • gas state • The lower the ionization energy, the easier it is to remove the electron • metals have low ionization energies • Ionization Energy decreases down the group • valence electron farther from nucleus • Ionization Energy increases across the period • left to right