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AP Chemistry Unit 3 - Elements

AP Chemistry Unit 3 - Elements. Lesson 9 – Quantum Numbers Book Section: 6.4-6.9. Quantum Numbers. Solving the wave equation gives a set of wave functions, or orbitals , and their corresponding energies. Each orbital describes a spatial distribution of electron density.

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AP Chemistry Unit 3 - Elements

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  1. AP ChemistryUnit 3 - Elements Lesson 9 – Quantum Numbers Book Section: 6.4-6.9

  2. Quantum Numbers • Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers.

  3. Principal Quantum Number (n) • The principal quantum number, n, describes the energy level on which the orbital resides. • The values of n are integers 1 and above. • n = 1, 2, 3…

  4. Angular Momentum Quantum Number (l) • This quantum number defines the shape of the orbital. • Allowed values of l are integers ranging from 0 to n – 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.

  5. Magnetic Quantum Number (ml) • The magnetic quantum number describes the three-dimensional orientation of the orbital. • Allowed values of mlare integers ranging from –l to +l: • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

  6. Magnetic Quantum Number (ml) • Orbitals with the same value of n form a shell. • Different orbital types within a shell are subshells.

  7. s Orbitals • The value of l for s orbitals is 0. • They are spherical in shape. • The radius of the sphere increases with the value of n.

  8. s Orbitals • Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n-1 nodes, or regions where there is 0 probability of finding an electron.

  9. p Orbitals • The value of l for p orbitals is 1. • They have two lobes with a node between them.

  10. d Orbitals • The value of l for a d orbital is 2. • Four of the five d orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

  11. Energies of Orbitals • For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. • That is, they are degenerate.

  12. Energies of Orbitals • As the number of electrons increases, though, so does the repulsion between them. • Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

  13. Spin Quantum Number, ms • In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. • The “spin” of an electron describes its magnetic field, which affects its energy.

  14. Spin Quantum Number, ms • This led to a fourth quantum number, the spin quantum number, ms. • The spin quantum number only has 2 allowed values: +1/2 and -1/2.

  15. Pauli Exclusion Principle • No two electrons in the same atom can have exactly the same energy. • Therefore, no two electrons in the same atom can have identical sets of quantum numbers.

  16. Sample Question • Predict the number of subshells in the fourth shell, that is, for n = 4. • Give the label for these subshells. • How many orbitals are in each of these subshells?

  17. Sample Question • Predict the number of subshells in the fourth shell, that is, for n = 4. • 4 (l = 0, 1, 2, 3) • Give the label for these subshells. • s, p, d, f • How many orbitals are in each of these subshells? • s – 1 • p – 3 • d – 5 • f – 7

  18. AP Questions • 1994 MC #27: Which of the following sets of quantum numbers (n, l, ml, ms) best describes the valence electron of highest energy in a ground-state gallium atom (atomic number 31)? • 4, 0, 0, ½ • 4, 0, 1, ½ • 4, 1, 1, ½ • 4, 1, 2, ½ • 4, 2, 0, ½

  19. AP Questions • 1994 MC #27: Which of the following sets of quantum numbers (n, l, ml, ms) best describes the valence electron of highest energy in a ground-state gallium atom (atomic number 31)? • 4, 0, 0, ½ • 4, 0, 1, ½ • 4, 1, 1, ½ - 48% correct, medium • 4, 1, 2, ½ • 4, 2, 0, ½

  20. AP Questions • 1984 MC #70: One of the outermost electrons in a strontium atom in the ground state can be described by which of the following sets of four quantum numbers? • 5, 2, 0, ½ • 5, 1, 1, ½ • 5, 1, 0, ½ • 5, 0, 1, ½ • 5, 0, 0, ½

  21. AP Questions • 1984 MC #70: One of the outermost electrons in a strontium atom in the ground state can be described by which of the following sets of four quantum numbers? • 5, 2, 0, ½ • 5, 1, 1, ½ • 5, 1, 0, ½ • 5, 0, 1, ½ • 5, 0, 0, ½ - 41% correct, medium

  22. HW: 6.48, 50, 52, 54, 56, 58 • This Week: • Thursday – Gravimetric Analysis of a Chloride Salt, Quantitative Analysis of Soluble Sulfate Due • Friday – Electron Configurations (6.4-6.9) • 10/18 – Gravimetric Analysis of a Chloride Salt Due • 10/20 – Elements Exam • 10/21 – Problem Set 2 Due

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