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  1. 1. Unit IV: Quantum Mechanics and Bonding QBA Miguel A. Castro Ramírez
  2. 2. Light• Before 1900, scientists thought that light behaved only as wave• discovered that also has particle-like characteristics
  3. 3. Light as a Wave• electromagnetic radiation: – form of energy that acts as a wave as it travels – includes: visible light, X rays, ultraviolet and infrared light, microwaves, and radio waves• All forms are combined to form electromagnetic spectrum
  4. 4. Light as a Wave
  5. 5. Light as a Wave• all form of EM radiation travel at a speed of 3.0 x 108 m/s in a vacuum• it has a repetitive motion• wavelength: (λ) distance between points on adjacent waves; in nm (109nm = 1m)• frequency: (ν) number of waves that passes a point in a second, in waves/secondInversely proportional! c = λυ
  6. 6. Photoelectric Effect• when light is shone on a piece of metal, electrons can be emitted• no electrons were emitted if the light’s frequency was below a certain value• scientists could not explain this with their classical theories of light• Ex: coin-operated sift drink machine
  7. 7. Photoelectric Effect• Max Planck: a German physicist• suggested that an object emits energy in the form of small packets of energy called quanta• quantum- the minimum amount of energy that can be gained or lost by an atom E = hνPlanck’s constant (h): 6.626 x 10-34 J*s
  8. 8. Photoelectric Effect• Einstein added on to Planck’s theory in 1905• suggested that light can be viewed as stream of particles• photon- particle of EM radiation having no mass and carrying one quantum of energy• energy of photon depends on frequency
  9. 9. Photoelectric Effect• EM radiation can only be absorbed by matter in whole numbers of photons• when metal is hit by light, an electron must absorb a certain minimum amount of energy to knock the electron loose• this minimum energy is created by a minimum frequency• since electrons in different metal atoms are bound more or less tightly, then they require more or less energy
  10. 10. H Line-Emission Spectrum• ground state- lowest energy state of an atom• excited state- when an atom has higher potential energy than it has at ground state• line-emission spectrum- series of wavelengths of light created when visible portion of light from excited atoms is shined through a prism
  11. 11. H Line-Emission Spectrum• scientists using classical theory expected atoms to be excited by whatever energy they absorbed• continuous spectrum- emission of continuous range of frequencies of EM radiation
  12. 12. H Line-Emission Spectrum• Why had hydrogen atoms only given off specific frequencies of light? current Quantum Theory attempts to explain this using a new theory of atom
  13. 13. H Line-Emission Spectrum• when an excited atom falls back to ground state, it emits photon of radiation• the photon is equal to the difference in energy of the original and final states of atom• since only certain frequencies are emitted, the differences between the states must be constant
  14. 14. Bohr Model• created by Niels Bohr (Danish physicist) in 1913• linked atom’s electron with emission spectrum• electron can circle nucleus in certain paths, in which it has a certain amount of energy
  15. 15. Bohr Model• Can gain energy by moving to a higher rung on ladder• Can lose energy by moving to lower rung on ladder• Cannot gain or lose while on same rung of ladder
  16. 16. Bohr Modela photon is releasedthat has an energyequal to thedifference betweenthe initial and finalenergy orbits
  17. 17. Bohr Model• problems: – did not work for other atoms – did not explain chemical behavior of atoms
  18. 18. Introduction to Quantum Theory• Quantum Theory- describes mathematically the wave properties of electrons
  19. 19. Electrons as Waves• In 1924, Louis de Broglie (French scientist)• suggested the way quantized electrons orbit the nucleus is similar to behavior of wave• electrons can be seen as waves confined to the space around a nucleus• waves could only be certain frequencies since electrons can only have certain amounts of energy
  20. 20. Electrons as Waves c c = λv v= λ hc E= λ E = hv h hcλ= = mc 2 mv λ E = mc 2shows that anything with both mass and velocityhas a corresponding wavelength
  21. 21. Uncertainty Principle• In 1927 by Werner Heisenberg (German theoretical physicist)• electrons can only be detected by their interaction with photons• any attempt to locate a specific electron with a photon knocks the electron off course• Heisenberg Uncertainty Principle- it is impossible to know both the position and velocity of an electron
  22. 22. Schrödinger Wave Equation• In 1926, Erwin Schrödinger (Austrian physicist)• his equation proved that electron energies are quantized• only waves of specific energies provided solutions to his equation• solutions to his equation are called wave functions
  23. 23. Schrödinger Wave Equation• wave functions give only the probability of finding an electron in a certain location• orbital- 3D area around a nucleus that has a high probability of containing an electron• orbitals have different shapes and sizes
  24. 24. Quantum Numbers• specify the properties of atomic orbitals and of electrons in orbitals• the first three numbers come from the Schrödinger equation and describe: – main energy level – shape – orientation• 4th describes state of electron
  25. 25. 1 Quantum Number stPrincipal Quantum Number: n• main energy level occupied by electron• values are all positive integers (1,2,3,…)• As n increases, the electron’s energy and its average distance from the nucleus increase• multiple electrons are in each level so have the same n value• the total number of orbitals in a level is equal to n2
  26. 26. 1 Quantum Number stEnergy
  27. 27. 2 Quantum Number ndAngular Momentum Quantum Number: l• indicates the shape of the orbital (sublevel)• the possible values of l are 0 to n-1• each atomic orbital is designated by the principal quantum number followed by the letter of the sublevel
  28. 28. 2 Quantum Number nds orbitals:• spherical• l value of 0• Max 2 electronsd
  29. 29. 2 Quantum Number ndp orbitals:• dumbbell-shaped• l value of 1• Max. 6 electrons
  30. 30. 2 Quantum Number ndd orbitals:• various shapes• l value of 2• Max. 10 electrons
  31. 31. 2 Quantum Number ndf orbitals:• various shapes• l value of 3• Max. 14 electrons
  32. 32. 2 Quantum Number ndLevel Sublevels Sublevels 0 1 2 3 0 1 2 0 1 0
  33. 33. 3 Quantum Number rdMagnetic Quantum Number: ml• indicates the orientation of an orbital around the nucleus• has values from -l +l• specifies the exact orbital that the electron is contained in• each orbital holds maximum of 2 electrons
  34. 34. Energy Sublevels # Orbitals Total # of Level in Level in Orbitals in (n) Sublevel Level 1 l=0, s 1 1 2 l=0, s 1 4 l=1, p 3 3 l=0, s 1 9 l=1, p 3 l=2, d 5 4 l=0, s 1 16 l=1, p 3 l=2, d 5 l=3, f 7
  35. 35. 4 Quantum Number thSpin Quantum Number: ms• indicates the spin state of the electron• only 2 possible directions• only 2 possible values: -½ and +½• paired electrons must have opposite spins
  36. 36. Energy Level 1n l ml ms1 0 0 -½,+½
  37. 37. Energy Level 2n l ml ms2 0 0 -½,+½ 1 -1 -½,+½ 0 -½,+½ +1 -½,+½
  38. 38. Energy Level 3n l ml ms3 0 0 -½,+½ 1 -1 -½,+½ 0 -½,+½ +1 -½,+½ 2 -2 -½,+½ -1 -½,+½ 0 -½,+½ +1 -½,+½ +2 -½,+½
  39. 39. Energy Level 4n l ml ms l ml ms4 0 0 -½,+½ 3 -3 -½,+½ 1 -1 -½,+½ -2 -½,+½ 0 -½,+½ +1 -½,+½ -1 -½,+½ 2 -2 -½,+½ 0 -½,+½ -1 -½,+½ +1 -½,+½ 0 -½,+½ +2 -½,+½ +1 -½,+½ +2 -½,+½ +3 -½,+½
  40. 40. Homework1. Give the values of n, ℓ, mℓ and ms for every orbital with n = 6.2. Indicate whether the set of quantum numbers (n, ℓ, mℓ) exits or not. a. 1, 1, 0 e. 8, 1, 0 b. 5, 4, –3 f. –2, 1, +1 c. 3, 2, –3 g. 4, 2, –1 d. 6, 7, +7 h. 7, 3, +43. Draw the shapes (including the orientation) of all the s, p and d orbitals.
  41. 41. Homework4. Which orbital in each of the following pairs is higher in energy? a. 5s or 5d b. 4s or 3p c. 6s or 4d5. What is the maximum number of electrons in an atom that can have these quantum numbers? a) n = 2 b) n = 3, c) n = 3, l = 1 d) n = 4, l = 2 e) n = 5, l= 3, ml=3