Electron Orbitals

1. Electron Orbitals Cartoon courtesy of lab-initio.com

2. Quantum MechanicalModel of the Atom Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found. These laws are beyond the scope of this class…

3. Heisenberg Uncertainty Principle “One cannot simultaneously determine both the position and momentum of an electron.” The more certain you are about where the electron is, the less certain you can be about where it is going. The more certain you are about where the electron is going, the less certain you can be about where it is. Werner Heisenberg

4. Quantum Numbers Each electron in an atom has a unique set of 4 quantum numbers which describe it. • Principal quantum number • Angular momentum quantum number • Magnetic quantum number • Spin quantum number

5. Electron Energy Level (Shell) Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. “n” is also known as the Principle Quantum number Number of electrons that can fit in a shell: 2n2

6. Electron Orbitals An orbital is a region within an energy level where there is a probability of finding an electron. Orbital shapes are defined as the surface that contains 90% of the total electron probability. The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located.

7. sOrbital shape The s orbital (l = 0) has a spherical shape centered around the origin of the three axes in space.

8. porbital shape There are three dumbbell-shaped porbitals(l = 1) in each energy level above n = 1, each assigned to its own axis (x, y and z) in space.

9. Things get a bit more complicated with the five d orbitals(l = 2) that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells” d orbital shapes …and a “dumbell with a donut”!

10. Shape of f (l = 3) orbitals

11. Energy Levels, Sublevels, Electrons

12. Magnetic Quantum Number The magnetic quantum number, generally symbolized by m, denotes the orientation of the electron’s orbital with respect to the three axes in space.

13. Orbital filling table

14. Electron Spin The Spin Quantum Numberdescribes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin:

15. Pauli Exclusion Principle Two electrons occupying the same orbital must have opposite spins Wolfgang Pauli

16. Assigning the Numbers • The three quantum numbers (n, l, and m) are integers. • The principal quantum number (n) cannot be zero. • n must be 1, 2, 3, etc. • The angular momentum quantum number (l) can be any integer between 0 and n - 1. • For n = 3, l can be either 0, 1, or 2. • The magnetic quantum number (ml) can be any integer between -l and +l. • For l = 2, m can be either -2, -1, 0, +1, +2.

19. Aufbau Principle Electrons will fill up lower energy levels first

20. Hund’s Rule Electrons in the same subshell occupy available orbitals singly before pairing up

21. The ELECTRON: Wave – Particle Duality Graphic: www.lab-initio.com

22. The Dilemma of the Atom • Electrons outside the nucleus are attracted to the protons in the nucleus • Charged particles moving in curved paths lose energy • What keeps the atom from collapsing?

23. Wave-Particle Duality JJ Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave!

24. The Wave-like Electron The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves. Louis deBroglie

25. Electromagnetic radiation propagates through space as a wave moving at the speed of light. c =  c = speed of light, a constant (3.00 x 108 m/s)  = frequency, in units of hertz (hz, sec-1)  = wavelength, in meters

26. The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation. E = h E= Energy, in units of Joules (kg·m2/s2) h= Planck’s constant (6.626 x 10-34 J·s) = frequency, in units of hertz (hz, sec-1)

27. Long Wavelength = Low Frequency = Low ENERGY Wavelength Table Short Wavelength = High Frequency = High ENERGY

28. The Electromagnetic Spectrum

29. Electron transitionsinvolve jumps of definite amounts ofenergy. This produces bands of light with definite wavelengths.

30. Electron Energy in Hydrogen Z= nuclear charge (atomic number) n= energy level ***Equation works only for atoms or ions with 1 electron (H, He+, Li2+, etc).

31. Calculating Energy Change, E, for Electron Transitions Energy must be absorbed from a photon (+E) to move an electron away from the nucleus Energy (a photon) must be given off (-E) when an electron moves toward the nucleus

32. Emission vs Absorption Spectra

33. Flame Tests Many elements give off characteristic light which can be used to help identify them. strontium sodium lithium potassium copper

34. Periodic Trends

35. Atomic Radius Definition: Half of the distance between nuclei in covalently bonded diatomic molecule • Radius decreases across a period • Increased effective nuclear charge due to decreased shielding • Radius increases down a group • Each row on the periodic table adds a “shell” or energy level to the atom

36. Table of Atomic Radii

37. Period Trend:Atomic Radius

38. Definition: the energy required to remove an electron from an atom Ionization Energy • Increases for successive electrons taken from the same atom • Tendsto increase across a period • Electrons in the same quantum level do not shield as effectively as electrons in inner levels • Irregularities at half filled and filled sublevels due to extra repulsion of electrons paired in orbitals, making them easier to remove • Tends to decrease down a group • Outer electrons are farther from the nucleus and easier to remove

39. Ionization Energy: the energy required to remove an electron from an atom • Increases for successive electrons taken from the same atom • Tends to increase across a period Electrons in the same quantum level do not shield as effectively as electrons in inner levels Irregularities at half filled and filled sublevels due to extra repulsion of electrons paired in orbitals, making them easier to remove • Tends to decrease down a group Outer electrons are farther from the nucleus

40. Table of 1st Ionization Energies

41. Periodic Trend:Ionization Energy

42. Electron Affinity Definition - the energy change associated with the addition of an electron • Affinity tends to increase across a period • Affinity tends to decrease as you go down in a period Electrons farther from the nucleus experience less nuclear attraction Some irregularities due to repulsive forces in the relatively small p orbitals

43. Periodic Trend:Electron Affinity

44. Electronegativity Definition: A measure of the ability of an atom in a chemical compound to attract electrons • Electronegativity tends to increase across a period • As radius decreases, electrons get closer to the bonding atom’s nucleus • Electronegativity tends to decrease down a group or remain the same • As radius increases, electrons are farther from the bonding atom’s nucleus

45. Periodic Table of Electronegativities

46. Periodic Trend:Electronegativity

47. Summary of Periodic Trends

48. Ionic Radii • Positively charged ions formed when • an atom of a metal loses one or • more electrons Cations • Smaller than the corresponding • atom • Negatively charged ions formed • when nonmetallic atoms gain one • or more electrons Anions • Larger than the corresponding • atom

49. Table of Ion Sizes