Sventae

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Sventae

  1. 1. Module 2.2: The Modern Atomic Theory and Quantum Mechanics Veronica Calindas, R.C. Adamson University 1 This lecture is based on textbooks authored by Chang, Brown & Holme, and Redmore
  2. 2. Modern Atomic Theory (from Dalton’s Hypotheses) 1. All matter is composed of atoms. The atom is the smallest body that retains the unique identity of the element. 2. Atoms of one element cannot be converted into atoms of another element in a chemical reaction. Elements can only be converted into other elements in nuclear reactions.
  3. 3. Modern Atomic Theory (from Dalton’s Hypotheses) 3. All atoms of an element have the same number of protons and electrons, which determines the chemical behavior of the element. Isotopes of an element differ in the number of neutrons, and thus in mass number. A sample of the element is treated as though its atoms have an average mass. 4. Compounds are formed by the chemical combination of two or more elements in specific ratios.
  4. 4. The Atom and its Subatomic Particles
  5. 5. Properties of Subatomic Particles Properties of the Three Key Subatomic Particles Charge Mass Relative 1+ 0 1- Absolute (C)* +1.60218 x 10-19 0 -1.60218 x 10-19 Relative (amu)† 1.00727 1.00866 0.00054858 Absolute (g) 1.67262 x 10-24 1.67493 x 10-24 9.10939 x 10-28 Location in the Atom Nucleus Outside Nucleus Nucleus Name (Symbol) Electron (e-) Neutron (n0) Proton (p+) Table 2.2 * The coulomb (C) is the SI unit of charge. † The atomic mass unit (amu) equals 1.66054 x 10-24 g.
  6. 6. Atomic Number, Mass Number and Isotopes Atomic Number (Z) = number of protons present in the nucleus of each atom of an element. Mass Number (A) = total number of neutrons and protons present in the nucleus of an atom of an element.
  7. 7. Atomic Number, Mass Number and Isotopes
  8. 8. Atomic Number, Mass Number and Isotopes  In some cases, atoms that have the same atomic number but different mass numbers exist. These are called isotopes.
  9. 9. Sample Problem: (1) Give the number of protons, neutrons and electrons in each of these species: a) 82Pb b) 29Cu c) 80Hg d) 80Hg ANSWERS: a) 82, 125, 82 b)29, 34, 29 c) 80, 119, 80, d) 80, 120, 80 207 63 199 200
  10. 10. Molecules and Ions  Molecules – an aggregate of at least two atoms in a definite arrangement held together by chemical forces (chemical bonds) -may contain atoms of the same element or atoms of two or more elements. • Ions – an atom or a group of atoms that has either a net positive or net negative charge. - only e- are either lost or gained during chemical changes
  11. 11. Molecules  Monoatomic molecules – those that exist as single atoms e.g. Group 8A Noble Gases  Diatomic molecules – those that contains only two atoms. e.g. N2, O2, and most of Group 7A Halogens  Polyatomic molecules – those that contain more than two atoms
  12. 12. Ions  Cation (X+) – an ion with positive net charge due to loss of electron  Anion (X-) – an ion with negative net charge due to gaining of electron Na 11 protons 11 electrons Na+ 11 protons 10 electrons Cl 17 protons 17 electrons Cl- 17 protons 18 electrons
  13. 13. Ions  Monoatomic ions– an ion that contains only one atom e.g. Na+, Mg2+, Fe3+, S2-, N3-  Polyatomic ions – an ion containing more than one atom e.g. OH-, CN-, NH4+
  14. 14. Sample Problem: (1) Give the number of protons, neutrons and electrons in each of these species: a) K+ b) Mg2+ c) Fe3+ d) Br- e) Mn2+ f) C-4 ANSWERS: a) 11, 12, 10 b) 12, 12, 10 c) 26, 29, 23 d) 35, 45, 36 e) 25, 30, 23 f) 6, 6, 10
  15. 15. The Duality of Electron  Erwin Schrödinger wrote a complicated mathematical equation that incorporates both particle behavior and wave behavior of an electron with respect to its probable location in the space of the system.  Schrödinger’s equation for hydrogen atom gave birth to a new era in physics and chemistry, this new field is called quantum mechanics Eψ = -h2 8π2μ {∂2ψ ∂x2 + ∂2ψ ∂y2 +∂2ψ ∂z2 { +V(x,y,z)ψ
  16. 16. The Schrödinger Equation Wave function ( ) describes: 1. energy of e- with a given 2. probability of finding e- in a volume of space Schrödinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.
  17. 17. The Four Quantum Numbers  Derived from Schrödinger’s equation for the hydrogen atom  Quantum numbers are required to describe the distribution of e- in hydrogen and other atoms, and the behavior of a specific e-. 17
  18. 18. The Four Quantum Numbers 1. Principal Quantum Number (n) 2. Azimuthal or Angular Momentum Quantum Number (l ) 3. Magnetic Quantum Number (ml ) 4. Spin Quantum Number (ms) 18
  19. 19. Principal Quantum Number (n)  Relates to the average distance of an e- from the nucleus in a particular orbital  Determines the energy of an orbital  Values are whole numbers only 19
  20. 20. The Schrödinger Equation 20 fn(n, l, ml, ms) principal quantum number n Where n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e- from the nucleus
  21. 21. Where 90% of the e- density is found for the 1s orbital Principal Quantum Number (n)
  22. 22. Angular Momentum Quantum Number (l)  Determines the shape of an orbital  The value of l depends on the value of n (from 0 to n-1) ◦ 0  s  spherical ◦ 1  p  dumb-bell ◦ 2  d  clover leaf ◦ 3  f  Subshell – one or more atomic orbitals having the same n and l values 22
  23. 23. The Schrödinger Equation 23 fn(n, l, ml, ms) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 Thus, if n = 1, then l = 0 n = 2, then l = 0 or 1 n = 3, then l = 0, 1, or 2 Shape of the “volume” of space that the e- occupies
  24. 24. Orbital ‘Shapes’ Based on l Values l = 0 (s orbitals) l = 1 (p orbitals)
  25. 25. Orbital ‘Shapes’ Based on l Values l = 2 (d orbitals)
  26. 26. Orbital ‘Shapes’ Based on l Values l = 3 (f orbitals)
  27. 27. Magnetic Quantum Number (ml)  Describes the orientation of the orbital in space  Values depend on the l (values are denoted as –l, 0, +l)  For a subshell of quantum number l, there is a total of 2l + 1 atomic orbitals within that subshell. Atomic orbitals within the same subshell have essentially the same energy. 27
  28. 28. The Schrödinger Equation 28 fn(n, l, ml, ms) magnetic quantum number ml for a given value of l ml = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), then ml = -1, 0, or 1 if l = 2 (d orbital), then ml = -2, -1, 0, 1, or 2
  29. 29. Orbital ‘Orientation’ Based on ml Values ml = -1 ml = 0 ml = 1
  30. 30. Orbital ‘Orientation’ Based on ml Values ml = -2 ml = -1 ml = 0 ml = 1 ml = 2
  31. 31. Atomic Orbitals 31
  32. 32. Atomic Orbitals 32
  33. 33. Spin Quantum Number (ms) 33  Emission spectra showed that the lines can be split by applying an external magnetic field.  According to Electromagnetic Theory, a spinning charge generates a magnetic spin, which causes the e- to behave like a magnet.  There are 2 possible values for motion of e-: clockwise (+ ½ ) or counter clockwise (– ½ )
  34. 34. The Schrödinger Equation 34 fn(n, l, ml, ms) spin quantum number ms where the only possible values are either +½ or -½ ms = -½ms = +½
  35. 35. Sample Problem:  List the values of n, l, and ml for orbitals of the following subshells: (1) 4d (2) 6p (3) 4s (4) 5f ANSWERS: (1) n=4, l=2, ml=7 ,(2) n=6, l=1, ml=3, (3) n=4, l=0, ml=1, (4) n=5, l=3, ml=7
  36. 36. Sample Problem:  What is the total number of orbitals associated with the following principal number? (1) n = 3 (2) n = 5 (3) n = 2 (4) n = 4 ANSWERS: (1) 9; (2) 19; (3) 7; (4) 16
  37. 37. Electron Configuration  Describes how the electrons are distributed among the various atomic orbitals.  A shorthand way of writing the quantum numbers for a specific atom
  38. 38. Electron Configuration: Orbital Diagram Example: Hydrogen atom: n=1, l=0, ml=0 1s1 principal quantum number n angular momentum quantum number l number of electrons in the orbital or subshell 1s1 H Then, the arrow-box configuration would yield: Upward spin = +½ Downward spin = -½
  39. 39. Rules for Writing an Electron Configuration 1) From the modern Atomic Theory, in a neutral atom, the number of protons equal to the number of electrons. If Atomic number = number of protons and Number of protons = number of electrons, then Atomic number = number of electron (for atoms with no charge) Only 2 electrons can occupy any subshell.
  40. 40. Rules for Writing an Electron Configuration 2) No two electrons in the same atom can have the same four quantum numbers (Pauli exclusion principle). ◦ If two electrons have the same n, l, and ml then they MUST have different values for ms – meaning, they must have opposite spins Example: 1s2 He 1s21s2 (a) (b) (c)
  41. 41.  Paramagnetism – when the two electrons have parallel spins  Paramagnetic substances are attracted to magnets. The Pauli Exclusion Principle 1s2 He 1s2
  42. 42.  Diamagnetism – when the two electrons in a single orbital have opposite spins  Diagmagnetic substances are slightly repelled by magnets. He 1s2 REMEMBER: Any atom with an odd number of electrons must be paramagnetic. On the other hand, atoms that have an even number of electrons can either be paramagnetic or diamagnetic. The Pauli Exclusion Principle
  43. 43. 3) The most stable arrangement of electrons in subshells is the one with the greatest parallel spins (Hund’s Rule of Multiplicity). Example: Nitrogen (Z=7) is 1s2 2s2 2p3, therefore the electron distribution as denoted by the arrow-box configuration would be Rules for Writing an Electron Configuration N 1s2 2s2 2px 2py 2pz
  44. 44. Example: Be (Z=4) is 1s2 2s2, therefore a diamagnetic Rules for Writing an Electron Configuration Be 1s2 2s2 Example: Si (Z=14) is 1s2 2s2 2p6 3s2 3p2 and thus, a paramagnetic Si 1s2 2s2 2px 2py 2pz 3s2 3px 3py 3pz
  45. 45. 4) An electron occupies the lowest energy orbital first before going to the next energy level (Aufbau principle). Rules for Writing an Electron Configuration 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
  46. 46. H 1 electron H 1s1 He 2 electrons He 1s2 Li 3 electrons Li 1s22s1 Be 4 electrons Be 1s22s2 B 5 electrons B 1s22s22p1 C 6 electrons ? ? 46
  47. 47. C 6 electrons C 1s22s22p2 N 7 electrons N 1s22s22p3 O 8 electrons O 1s22s22p4 F 9 electrons F 1s22s22p5 Ne 10 electrons Ne 1s22s22p6 47
  48. 48. The Shielding Effect in Many-Electron Atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s  The 1s lies at lower energy level than 2s and 2p in a many-electron atom • This means that the 2s and 2p electrons are partly ‘shielded’ from the nucleus’s attractive force by the much- closer 1s electron. •Because the stability of an electron is determined by the strength of its attraction to the nucleus, it follows that it will require less energy to remove an electron from 2p orbital than it would to remove the electron in 2s.
  49. 49. Problem:  Write the electronic configuration of the following: 1. Ne (Z= 10) 2. Sc (Z= 21) 3. Ru (Z= 44) 4. Pb (Z= 82) 5. W (Z= 74)
  50. 50. Valence Electrons  Electrons which occupies the outermost orbitals of an electron or the valence shell  Responsible for the reactions that an atom of an element can undergo 50
  51. 51. 7/21/2013 General Chemistry for Engineers 51
  52. 52. 7/21/2013 General Chemistry for Engineers 52
  53. 53. 7.87/21/2013 53General Chemistry for Engineers
  54. 54. What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s22s22p63s2 2 + 2 + 6 + 2 = 12 electrons Abbreviated as [Ne]3s2 [Ne] 1s22s22p6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s22s22p63s23p5 2 + 2 + 6 + 2 + 5 = 17 electrons Last electron added to 3p orbital n = 3 l = 1 ml = -1, 0, or +1 ms = ½ or -½ 54
  55. 55. 7/21/2013 55General Chemistry for Engineers
  56. 56. Classification of Groups of Elements in the Periodic Table Accd’g to Type of Outermost Subshell filled

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