Quantum Mechanics & Electron Configuration

1. Quantum Mechanics & Electron Configuration Chapter 5: Electrons in Atoms

2. Part 1: Models of the Atom 1897: Thompson Model (Plum Pudding) 1911: Rutherford Model – Small, dense, + charged nucleus Electrons orbit around 1913: Bohr Model 1926: Quantum Mechanical Model – Erwin Schrodinger & his math equations

3. Bohr Model (aka the versions you’ve learned before) • Electrons move around the nucleus in fixed spherical orbits with fixed energies • Fixed energies = orbits / energy levels • Aka rungs of a ladder • Electrons can go to a higher or lower energy level • Either gain or lose energy to move levels • Electrons CANNOT be between levels

4. Atomic Emission Spectra ** When atoms absorb energy (i.e. electric current), they move to a higher energy level … … these electrons emit light when they return back to a lower energy level • Emission spectra is unique for each element • The light emitted consists of only a mixture to specific frequencies… • If you pass the light through a slit and then a prism, you can separate the resulting light into its frequencies (aka colors) Barium

5. Light • Has properties of both:  a Particle ( ____________)  a Wave Light Waves: Amplitude: crest of the wave (height from 0) Wavelength: distance between crests (λ) Frequency: # of waves per unit time (ν) Units: Hertz (Hz) aka s-1

7. Math Time!!! c = λν C = speed of light (constant) = 2.998 x 108 m/s λ = Wavelength (m) ν = Frequency (Hz or s-1)

9. More Math… • The energy (E) of a photon is directly proportional to its frequency. Higher freq = More Energy Lower Freq = Less Energy E = h x v E = energy (joules – J) H = Plank’s constant = 6.626E-34 J/s v = Frequency (Hz or s-1)

10. Example: What is the energy of a quantum of light with a frequency of 7.39 x 1014 Hz?

11. Think about this… • E = h x v • c = λν What would you do if you were asked to solve for the frequency of light if you are given a wavelength of 700nm? What would you do if you were asked to find the energy of light if you are given a wavelength of 480nm?

12. Emission Spectra Lab Look at the gas tubes and follow directions provided.

13. Continuous Spectrum v. Line Spectrum • What did you observe in the Emission Lab?

14. Light has Wave-Particle Duality (& so do electrons) • Particle & Wave-like Nature • Depends on experiment / what we try to observe • Throws a wrench in Bohr Model… • New method of describing the motion of subatomic particles = foundation of quantum mechanics = movement/organization of subatomic particles

15. The Quantum Mechanical Model • This is what we use today • Describes: LOCATION & ENERGY of electrons • Electrons do not have a direct orbit around nucleus • Based on probability • Electron clouds • Electrons do have energy levels

16. Hog Hilton Sample Problem • Book 15 hogs into their rooms • 6th floor ____ ____ ____ _____ _____ • 6th floor ______ • 5th floor ______ ______ ______ • 4th floor ______ • 3rd floor ______ ______ ______ • 2nd floor ______ • 1st floor ______

17. Hog Hilton Sample ProblemPlace 15 electrons into their spaces • 3d_____ _____ _____ _____ ____ • 4s _____ • 3p ______ ______ ______ • 3s ______ • 2p ______ ______ ______ • 2s ______ • 1s ______

18. But…all of these electrons are not organized into hotel rooms, but ATOMIC ORBITALS

19. So, what exactly is an ATOMIC ORBITAL? Atomic Orbital = region of space in which there is a high probability of finding an electron • They come in different SHAPES, SIZES & ENERGY LEVELS!! • These are described by Quantum Numbers…

20. Part 2 Quantum Numbers Get ready…here we go…

21. Quantum Numbers Used to describe the location of electrons Electrons in an atom CANNOT have the same quantum numbers  Unique for each electron  Like an address

22. Principle Quantum Number (think…Energy Level) • n • Allowable values = 1, 2, 3 … n (positive, integer values) • Describes energy level • Position of the electron w/ respect to nucleus • As n increases = further from nucleus

23. Angular Momentum Quantum Number(Azimuthal Quantum Number)(think…energy sublevel)Pay attention…this is where it starts to get complicated • l • Allowed values: 0, 1, 2, … (n-1) • Describes the sublevel • SHAPE of the orbital • SHAPES: • l = 0 = s orbital = spherical cloud • l = 1 = p orbital = dumbbell cloud • l = 2 = d orbital = clover cloud • l = 3 = f orbital = … too complicated

24. Example • If I had a principal quantum number of 2, what are my possible angular momentum quantum numbers? n = 2 l =

25. Angular Momentum Quantum Number: Orbital Shapes

26. Magnetic Quantum Number (ml) • Determines spatial orientation (x, y, z, plane) • Possible Values: - l to + l • Examples: if it is a d orbital d orbital: l = ml =

27. Example: p-orbital n = 2 l = ml = This means, there are _______ p-orbitals and that they are in three directions (x, y, z axes):

28. What orbital corresponds to :n = 2l = 1ml = 0 Energy level = Sublevel = _____ - orbital Orientation: Orbital:

29. Number of orbitals within an energy level: n2 Examples: How many orbitals are in energy level 2? n = l = ml = Orbitals = • Each orbital holds 2 electrons:So, how many electrons can energy level 2 hold? # Electrons = 2n2

30. Spin Quantum Number • ms • Describes the direction of the electrons spin within an orbital (remember, each orbital only holds 2 electrons) • Possible Values: ½ or -½ (spin up, spin down) • Think back to hogs…

31. Ahhh…it’s too much information…HELP!!! • Solution: STUDY and PRACTICE!!!

32. Examples • n = 3 (what are the possible quantum numbers?) • What orbital corresponds to n = 4 & l = 2?

33. What orbital corresponds to n = 4 , l = 1, ml = -1 Energy Level = Sublevel = Orbital orientation = Orbital =

34. Re-iterate:

37. STOPDo You Have Any Questions?

38. PART 3 Rules of Electron Configuration

39. Aufbau Principle • Electrons enter orbitals of lowest energy first • Orbitals within a sublevel have equal energy (3px, 3py, 3pz) • Exceptions: Cr , Cu • Which hog rules is this?

40. Pauli Exclusion Principle • An atomic orbital may only hold two electrons • Electrons must have opposite spin • Clockwise or counterclockwise spin • Denoted with arrows • Prevents two electrons from having same quantum numbers • Which hog rule is this?

41. Hund’s Rule • Every orbital of the same energy is singly occupied before any orbital is doubly occupied • Electrons have the same spin • Second electrons added have opposite spins • Which hog rule is this?

42. PART 4 Writing Electron Configurations

43. Electron Configuration Diagonal Rule • Starting with the top arrow, follow the arrows one by one in the direction they point, listing the sublevels as you pass through them. • Stop when you get to the sublevel you need.

44. Electron Orbital Diagram 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

45. Example: Fill Orbitals w/ 7 electrons 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___

46. Review: • How many electrons fill an s orbital? • How many electrons fill a p orbital ?(remember subshells…) • How many electrons fill a d orbital? • How many electrons fill an f orbital?

47. Example: Cl 3d ___ ___ ___ ___ ___ 4s ___ 3p ___ ___ ___ 3s ___ 2p ___ ___ ___ 2s ___ 1s ___ Give the final E.C:

48. With a partner:Examples: Give the E.C • H • He • Li • Be • B • C • N • F

49. No more…Make it stop!@!!!! • Write the electron configuration for Barium: • Ahhhhhhhhhh!!! Too many electrons!! • But wait…there’s a shortcut… • Noble gas / shorthand configuration: • Find the nearest noble gas that came before the element you are interested in • Write the symbol of that noble gas in [brackets] • Write the configuration as normal from there…

50. Examples: Sb