Quantum Theory

1. http://www.colby.edu/chemistry/CH141F/Chapter%206%20presentation.ppthttp://www.colby.edu/chemistry/CH141F/Chapter%206%20presentation.ppt Quantum Theory Schrodinger Heisenberg http://staff.science.nus.edu.sg/~PC1144/PC1144%20Lectures/lecture16.ppt

2. The Quantum Mechanical Model • Energy is quantized. It comes in chunks. • A quanta is the amount of energy needed to move from one energy level to another. • Since the energy of an atom is never “in between” there must be a quantum leap in energy. • Schrodinger derived an equation that described the energy and position of the electrons in an atom

3. The Quantum Mechanical Model • Heisenberg Uncertainty Principle---it is impossible to know both the exact position and momentum of an object at the same time. • Can’t know position if e- is moving. • Can’t know momentum if e- is not moving.

4. The Quantum Mechanical Model • Has energy levels for electrons. • Orbits are not circular. • It can only tell us the probability of finding an electron a certain distance from the nucleus.

5. The Quantum Mechanical Model • The atom is found inside a blurry “electron cloud” • A area where there is a chance of finding an electron. • Draw a line at 90 %

6. Schrodinger’s Quantum #’s • (n) Principal quantum # n = 1, 2, 3 … -1 • the energy level of the electron. • Formula:2(n)2 = # of electrons per energy level • (l) Azimuthal or Secondary quantum # l = 0,1, 2, (n-1) • the sublevels or shapewithin an energy level. • s,p,d,f (names of sublevels) • s,p,d, & f each have a unique shape.

7. Quantum #’s (cont.) • (ml) magnetic quantum # ml = +l .. 0 .. –l (2l +1) = total orbitals • regions where there is a high probability of finding an electron • each orbital can hold 2 e- • (ms) spin quantum # ms = +1/2 or –1/2 • in each orbital there can be up to 2 electrons spinning in opposite directions. • Clockwise  +1/2 Counter clockwise  –1/2

8. Quantum Numbers s p d f

9. Arrangement of Electrons in Atoms Electrons in atoms are arranged as LEVELS (n) SUBLEVELS (l) ORBITALS (ml)

10. Energy Levels • Each energy level has a number called thePRINCIPAL QUANTUM NUMBER, n • Currently n can be 1 thru 7, because there are 7 periods on the periodic table

11. n = 1 n = 2 n = 3 n = 4 Energy Levels

12. Orbitals and the Periodic Table • Orbitals grouped in s, p, d, and f orbitals (sharp, proximal, diffuse, and fundamental) s orbitals d orbitals p orbitals f orbitals

13. s orbitals • 1 s orbital for every energy level • Spherical shaped • Each s orbital can hold 2 electrons • Called the 1s, 2s, 3s, etc.. orbitals. 3s 2s 1s

14. p orbitals • Start at the second energy level • 3 different directions • 3 different shapes • Each can hold 2 electrons

15. d orbitals • Start at the third energy level • 5 different shapes • Each can hold 2 electrons

16. f orbitals • Start at the fourth energy level • Have seven different shapes • 2 electrons per shape

17. f orbitals

18. Summary # of orbitals Max electrons Starts at energy level s 1 2 1 p 3 6 2 5 10 3 d 7 14 4 f

19. Number of Electrons that can be held in each orbital • s = 2 e- • p = 6 e- • d = 10 e- • f = 14 e-

20. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s

21. Electron Configurations • The way electrons are arranged in atoms. • Aufbau principle- electrons enter the lowest energy first. • This causes difficulties because of the overlap of orbitals of different energies. • Pauli Exclusion Principle- at most 2 electrons per orbital - different spins • Hund’s Rule- When electrons occupy orbitals of equal energy they don’t pair up until they have to .

22. Electron Configuration • Let’s determine the electron configuration for Phosphorus (P) • Need to account for 15 electrons

23. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s • The first to electrons go into the 1s orbital • Notice the opposite spins • only 13 more

24. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s • The next electrons go into the 2s orbital • only 11 more

25. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s • The next electrons go into the 2p orbital • only 5 more

26. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s • The next electrons go into the 3s orbital • only 3 more

27. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s • The last three electrons go into the 3p orbitals. • They each go into seperate shapes • 3 upaired electrons • 1s22s22p63s23p3

28. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s The easy way to remember • 1s2 • 2 electrons

29. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 • 4 electrons

30. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 2p6 3s2 • 12 electrons

31. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 2p6 3s2 3p6 4s2 • 20 electrons

32. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 • 38 electrons

33. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 • 56 electrons

34. 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s Fill from the bottom up following the arrows • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 • 88 electrons

35. Fill from the bottom up following the arrows 7s 7p 7d 7f 6s 6p 6d 6f • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s • 108 electrons

36. + + + + + Effective Nuclear Charge • Electrostatic repulsion between negatively charged electrons • Influences the energies of the orbitals. • The effect of repulsion is described as screening or shielding. • The combined effect of attraction to the nucleus and repulsion from other electrons gives an effective nuclear charge, Zeff, which is less than that of the ‘bare’ nucleus. Zeff = Z - S # Protons # Shielding electrons

37. Periodicity of Effective Nuclear Charge Z* on valence electrons

38. Effective Nuclear Charge, Zeff • Atom Zeff Experienced by Electrons in Valence Orbitals • Li +1 • Be +2 • B +3 • C +4 • N +5 • O +6 • F +7 Increase in Zeff across a period

39. Electron Configurations A list of all the electrons in an atom (or ion) • Must go in order (Aufbau principle) • 2 electrons per orbital, maximum • We need electron configurations so that we can determine the number of electrons in the outermost energy level. These are called valence electrons. • The number of valence electrons determines how many and what this atom (or ion) can bond to in order to make a molecule 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14…etc.

40. Electron Configurations 2p4 Number of electrons in the sublevel Energy Level Sublevel 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14…etc.

41. Let’s Try It! • Write the electron configuration for the following elements: H Li N Ne K Zn Pb

42. Shorthand Notation • A way of abbreviating long electron configurations • Since we are only concerned about the outermost electrons, we can skip to places we know are completely full (noble gases), and then finish the configuration

43. Shorthand Notation • Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ]. • Step 2: Find where to resume by finding the next energy level. • Step 3: Resume the configuration until it’s finished.

44. Shorthand Notation • Chlorine • Longhand is 1s2 2s2 2p6 3s2 3p5 You can abbreviate the first 10 electrons with a noble gas, Neon. [Ne] replaces 1s2 2s2 2p6 The next energy level after Neon is 3 So you start at level 3 on the diagonal rule (all levels start with s) and finish the configuration by adding 7 more electrons to bring the total to 17 [Ne] 3s2 3p5

45. Practice Shorthand Notation • Write the shorthand notation for each of the following atoms: Cl K Ca I Bi

46. Valence Electrons Electrons are divided between core and valence electrons B 1s2 2s2 2p1 Core = [He] , valence = 2s2 2p1 Br [Ar] 3d10 4s2 4p5 Core = [Ar] 3d10 , valence = 4s2 4p5

47. Rules of the Game No. of valence electrons of a main group atom = Group number (for A groups) Atoms like to either empty or fill their outermost level. Since the outer level contains two s electrons and six p electrons (d & f are always in lower levels), the optimum number of electrons is eight. This is called the octet rule.

48. Keep an Eye On Those Ions! • Electrons are lost or gained like they always are with ions… negative ions have gained electrons, positive ions have lost electrons • The electrons that are lost or gained should be added/removed from the highest energy level (not the highest orbital in energy!)

49. Keep an Eye On Those Ions! • Tin Atom: [Kr] 5s2 4d10 5p2 Sn+4 ion: [Kr] 4d10 Sn+2 ion: [Kr] 5s2 4d10 Note that the electrons came out of the highest energy level, not the highest energy orbital!

50. Keep an Eye On Those Ions! • Bromine Atom: [Ar] 4s2 3d10 4p5 Br- ion: [Ar] 4s2 3d10 4p6 Note that the electrons went into the highest energy level, not the highest energy orbital!