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Quantum Mechanics

Explore the concepts of quantum mechanics and atomic structure, including the electron cloud model, Schrödinger wave equation, quantum numbers, and orbital filling diagrams.

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Quantum Mechanics

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  1. Quantum Mechanics

  2. Atomic Structure • Electron Cloud Model • “Cloud” is a probability distribution. • Probability is the most information that we can possibly know.

  3. Schrödinger Wave Equation • Allows you to calculate the probability of an electron being in a given place and energy. • Gives us a good idea of where the electrons are in an atom.

  4. Quantum Numbers • Address of an electron in an atom • The collection of 4 quantum numbers gives you as much information as you can possibly get for a particular electron. • Describes a hierarchical structure • Shell • Subshell • Orbitals • Electron Spin States

  5. How far from the nucleus an electron is. Also describes most of the energy. Will be integers from 1 to 7 for our purposes. Call this the “shell” the electron is in. n = 1 (the first shell) is shell closest to nucleus with lowest energy n Principle Quantum Number

  6. Angular momentum describes movement in circles. Describes the shape of the area an electron is in. Can be integers from 0 through 3 Usually called the “sub-shell” ℓ Angular Momentum Quantum Number A cursive L

  7. Angular Momentum Quantum Number • Specific Values have specific names • ℓ = 0 is called an s subshell • ℓ = 1 is called a p subshell • ℓ = 2 is called a d subshell • ℓ = 3 is called a f subshell

  8. s Orbitals within an s Subshell • Have a spherical shape

  9. p Orbitals within a p Subshell • Have a dumbbell shape

  10. d Orbitals within a d Subshell • Have a four leaf clover shape

  11. f Orbitals within an f Subshell • Look like two d orbitals pushed together in the middle

  12. Describe which direction the shapes point in space. Refers to specific orbitals Orbital – area of space analogous to an orbit but taking probability into account Each orbital holds up to two electrons. mℓ Magnetic Quantum Number m with a subscript L

  13. Magnetic Quantum Number • Only one direction in space for a sphere • Only one s orbital

  14. Magnetic Quantum Number • There are three directions for p orbitals to point • There are three p orbitals

  15. Magnetic Quantum Number • There are five solutions for the d orbitals

  16. Magnetic Quantum Number • Seven f orbitals

  17. Magnetic Quantum Number • n = 1 is where the s subshells start • n = 2 is where the p subshells start • n = 3 is where the d subshells start • n = 4 is where the f subshells start

  18. Describes the spin of an electron Imagine a top spinning on its axis Can either be +½ or -½ ms Spin Quantum Number m with a subscript s

  19. For the Math People • For a given electron • n = [1, 2, 3, 4, 5, 6, or 7] • ℓ = [0, … n – 1] • mℓ = [-ℓ … +ℓ] • ms = [-½, +½]

  20. How do we apply all this to electrons? • Aufbau Principle – fill up electrons in the lowest energy first • Use the diagonal line diagram.

  21. Hydrogen • Start with the simplest atom. • Has one electron

  22. Orbital Filling Diagrams • Use horizontal lines to represent an orbital • Use half arrows to represent electrons • Arrow up means spin +½ • Arrow down means spin -½

  23. Helium • Has two electrons • Where do you put the extra electron? • Pauli Exclusion Principle – No two electrons in the same atom can have the same set of four quantum numbers • Practically this means two electrons in the same orbital must have opposite spins.

  24. More Elements • Lithium • Three electrons • Beryllium • Four electrons

  25. Boron • 5 electrons • Does it matter which p-orbital you put the electron in? • No because they are all equivalent • Degenerate – have the same energy

  26. Carbon • Six electrons • Where does the sixth electron go? • Hund’s Rule – Electrons stay unpaired as long as possible.

  27. More Elements • Nitrogen • 7 electrons • Oxygen • 8 electrons • Fluorine • 9 electrons • Neon • 10 electrons

  28. More Elements • Chromium • Krypton

  29. More Elements • Tin • Promethium

  30. Even More Elements • Tungsten • Lead

  31. Even More Elements • Plutonium • Bohrium

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