2. M ODELS OF THE A TOM Beginning with Rutherford

3. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC P ROBLEMS WITH R UTHERFORD ’ S M ODEL It didn’t explain WHY metals and metal compounds give off characteristic colors when they are flame tested It didn’t explain why metals glow when heated – first red, orange yellow and then white It didn’t explain the CHEMICAL properties of elements

4. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC B OHR ’ S T HEORY Electrons are located at specific energy levels surrounding the nucleus Each rung on the ladder represents an energy level The higher the energy level – the farther it is from the nucleus Bohr thought the electrons moved in fixed ORBITS around the nucleus – we know this is not true today

5. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC B OHR M ODEL First model of the electron structure Gives levels where an electron is most likely to be found Incorrect today, but a key in understanding the atom 4

6. Section 7.4 The Bohr Model Return to TOC 5 Bohr’s model gave hydrogen atom energy levels consistent with the hydrogen emission spectrum. Ground state – lowest possible energy state (n = 1) Bohr’s model is incorrect. This model only works for hydrogen. Electrons do not move around the nucleus in circular orbits. Electronic Transitions in the Bohr Model for the Hydrogen Atom a) An Energy-Level Diagram for Electronic Transitions Electronic Transitions in the Bohr Model for the Hydrogen Atom b) An Orbit- Transition Diagram, Which Accounts for the Experimental Spectrum

7. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC S CHRÖDINGER ' S T HEORY He agreed that electrons have a specific amount of energy He believed that the distance between rungs on the ladder were not consistent – they get closer together as you move higher up Quantum – the amount of energy needed to move from one energy level to another The electrons move in regions of probability around the nucleus called ORBITALS

8. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC Quantum theory, also called wave mechanics, describes the arrangement and space occupied by electrons. Orbitals refers to the three-dimensional regions in space where there is a high probability of finding an electron around an atom. 7

9. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC C HARACTERISTICS OF E LECTRONS Extremely small mass Located outside the nucleus Moving at extremely high speeds in a sphere Have specific energy levels 8

10. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC E NERGY OF E LECTRONS When atoms are heated, bright lines appear called line spectra Electrons in atoms arranged in discrete levels. An electron absorbs energy to “jump” to a higher energy level. When an electron falls to a lower energy level, energy is emitted. 9

11. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC L OSS AND G AIN OF E NERGY 10 GaInGaIn LossLoss

12. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC L EARNING C HECK Answer with 1) Energy absorbed2) Energy emitted 3) No change in energy A. What energy change takes place when an electron in a hydrogen atom moves from the first (n=1) to the second shell (n=2)? B. What energy change takes place when the electron moves from the third shell to the second shell? 11

13. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC S OLUTION A.1) Energy absorbed B.2) Energy emitted 12

14. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC R ELATIVE O RBITAL S IZE Difficult to define precisely. Orbital is a wave function. Picture an orbital as a three-dimensional electron density map. Hydrogen 1 s orbital:  Radius of the sphere that encloses 90% of the total electron probability. 13 We do not know the detailed pathway of an electron. The electrons move in regions of probability around the nucleus called ORBITALS

15. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC T HE ELECTRONS MOVE IN REGIONS OF PROBABILITY AROUND THE NUCLEUS CALLED ORBITALS D EFINING THESE ORBITALS: Quantum Numbers are used to define: The energy of the electron The electron’s relative distance from the nucleus The size and shape of the ORBITAL The pairings of the electrons

16. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC Q UANTUM N UMBERS Principle Quantum Number (n) – define the energy of the electron n=1 is closest to the nucleus – low energy n=2 is farther than n=1, slightly more energy n=3 is farther than n=1 and n=2, still increasing in energy n=4 ….. Remember – The difference in energy between energy levels decreases as “n” increases

17. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC S UBLEVELS Within each principle energy level (n) – there are sublevel(s). The larger the value of ‘n’, the more sublevels you can have. Sublevels – named by their shape s – sphere p – pear d- dumbbell f - fundamental

18. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC T WO R EPRESENTATIONS FOR AN S O RBITAL Figure 3.16, pg. 77 Investigating Chemistry, 2nd Edition © 2009 W.H. Freeman & Company

19. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC R EPRESENTATIONS FOR P ORBITALS E ACH ORBITAL CAN HOLD UP TO 2 ELECTRONS, REGARDLESS OF SHAPE. T HIS SET OF THREE ORBITALS HOLDS 6 ELECTRONS. Figure 3.17, pg. 77 Investigating Chemistry, 2nd Edition © 2009 W.H. Freeman & Company

20. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC T HERE IS A SET OF FIVE DIFFERENT D ORBITALS. T HERE IS A SET OF SEVEN F ORBITALS. E ACH ORBITAL REGARDLESS OF ITS SHAPE HOLDS 2 ELECTRONS.

21. Section 7.7 Orbital Shapes and Energies Return to TOC 20 1s Orbital

22. Section 7.7 Orbital Shapes and Energies Return to TOC 21 Two Representations of the Hydrogen 1s, 2s, and 3s Orbitals

23. Section 7.7 Orbital Shapes and Energies Return to TOC 22 2p x Orbital

24. Section 7.7 Orbital Shapes and Energies Return to TOC 23 2p y Orbital

25. Section 7.7 Orbital Shapes and Energies Return to TOC 24 2p z Orbital

26. Section 7.7 Orbital Shapes and Energies Return to TOC 25 The Boundary Surface Representations of All Three 2p Orbitals

27. Section 7.7 Orbital Shapes and Energies Return to TOC 26 3d x 2 -y 2 Orbital

28. Section 7.7 Orbital Shapes and Energies Return to TOC 27 3d xy Orbital

29. Section 7.7 Orbital Shapes and Energies Return to TOC 28 3d xz Orbital

30. Section 7.7 Orbital Shapes and Energies Return to TOC 29 3d yz Orbital

31. Section 7.7 Orbital Shapes and Energies Return to TOC 30 Orbital

32. Section 7.7 Orbital Shapes and Energies Return to TOC 31 The Boundary Surfaces of All of the 3d Orbitals

33. Section 7.7 Orbital Shapes and Energies Return to TOC 32 Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

34. Section 7.5 The Quantum Mechanical Model of the Atom Return to TOC S UBLEVELS Principle Energy Level Sublevel n= 1 s n=2 s and p n=3 s and p and d n=4 s, p, d, and f NOTICE: The value of ‘n’ tells you how many sublevels are present in that energy level

35. Section 7.6 Quantum Numbers Return to TOC 34 Principal quantum number (n) – size and energy of the orbital. Angular momentum quantum number (l) – shape of atomic orbitals (sometimes called a subshell). Magnetic quantum number (m l ) – orientation of the orbital in space relative to the other orbitals in the atom.

36. Q UANTUM N UMBERS FOR THE F IRST F OUR L EVELS OF O RBITALS IN THE H YDROGEN A TOM 35

37. Section 7.6 Quantum Numbers Return to TOC 36 Exercise For principal quantum level n = 3, determine the number of allowed subshells (different values of l), and give the designation of each. (hint refer to previous chart) # of allowed subshells = 3 l = 0, 3s l = 1, 3p l = 2, 3d

38. Section 7.6 Quantum Numbers Return to TOC 37 Exercise For l = 2, determine the magnetic quantum numbers (m l ) and the number of orbitals. (note refer to previous chart) magnetic quantum numbers = –2, – 1, 0, 1, 2 number of orbitals = 5

39. Section 7.7 Orbital Shapes and Energies Return to TOC Locating these on the Periodic Table Principle Energy Level (n) – is the period in the periodic table The Sublevels are located in specific regions – Color these together

40. Section 7.7 Orbital Shapes and Energies Return to TOC 39 The periodic table is structured so that elements with the same type of valence electron configuration are arranged in columns. The left-most columns include the alkali metals and the alkaline earth metals. In these elements the valence s orbitals are being filled On the right hand side, the right-most block of six elements are those in which the valence p orbitals are being filled In the middle is a block of ten columns that contain transition metals. These are elements in which d orbitals are being filled Below this group are two rows with 14 columns. These are commonly referred to the f-block metals. In these columns the f orbitals are being filled

41. Section 7.7 Orbital Shapes and Energies Return to TOC 40 The periodic table is structured so that elements with the same type of valence electron configuration are arranged in columns. Important facts to remember: 2, 6, 10 and 14 are the number of electrons that can fill the s, p, d and f subshells (the l=0,1,2,3 azimuthal quantum number) The 1s subshell is the first s subshell, the 2p is the first p subshell 3d is the first d subshell, and the 4f is the first f subshell

42. Section 7.7 Orbital Shapes and Energies Return to TOC Naming the sublevels 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f

43. Section 7.7 Orbital Shapes and Energies Return to TOC Orbitals Orbitals are regions of probability – each orbital can hold a maximum of 2 e- The ‘s’ sublevel has 1 orbital The ‘p’ sublevel has 3 orbitals The ‘d’ sublevel has 5 orbitals The ‘f’ sublevel has 7 orbitals

44. Section 7.7 Orbital Shapes and Energies Return to TOC Orbitals Do you have to memorize this? NO Look at the sublevel regions that you colored in on your periodic table.

45. Section 7.7 Orbital Shapes and Energies Return to TOC Orbitals Count how many electrons are in the ‘s’ sublevel 2 This means that since there are two electrons, and each orbital can hold two electrons, that there is only ONE orbital.

46. Section 7.7 Orbital Shapes and Energies Return to TOC Orbitals Count how many electrons are in the ‘p’ sublevel 6 This means that since there are six electrons, and each orbital can hold two electrons, that there are THREE orbitals.

47. Section 7.7 Orbital Shapes and Energies Return to TOC Orbitals Count how many electrons are in the ‘d’ sublevel 10 This means that since there are ten electrons, and each orbital can hold two electrons, that there are FIVE orbitals.

48. O RBITALS Count how many electrons are in the ‘f’ sublevel 14 This means that since there are fourteen electrons, and each orbital can hold two electrons, that there are SEVEN orbitals.