4.2 Chemistry Slides

1. Quantum Mechanical Model of the Atom BC High Chemistry Mr. Olejnik

2. Review of Atomic Models • Bohr’s Model • Electrons move in definate orbits or energy levels around the nucleus

3. Wave model of atom • Modern model of atom • According to theory of wave mechanics electrons don’t orbit nucleus predictably • Impossible to determine location of electron, we interpret it with a “cloud”.

4. Light as Waves • Wavelength = distance between the crests of two subsequent waves (wave = λ “lambda”) • Frequency = how often a wave crosses a fixed point (v)

5. Think • Which of the following has the longest wavelength (λ) • Which of the following has the highest frequency (v)

6. Speed of Light • Speed of light ≈ 3.00 x 108 m/s = C • C = λv • Λ & v are inversely proportional so if λ increases, v decreases etc.

7. Quantum Mechanical Model • Mathematical Model of the atom based on the Quantum Theory, • Quantum Theory basically says: • Matter has properties associated with waves. • Impossible to predict the exact position of e- • E- have both properties of particles & waves

8. Quantum Mechanical Model • Developed in the 1920’s • Werner Heisenberg (Uncertainty Principle) • Louis de Broglie (electron has wave properties) • Erwin Schrodinger (mathematical equations using probability, quantum numbers)

9. Werner Heisenberg: Uncertainty Principle • We can not know both the position and momentum of a particle at a given time.

10. Louis de Broglie, (France, 1892-1987)Wave Properties of Matter (1923) • Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior. • de Broglie wavelength l= h mv

11. Particle vs. Wave • Is light particles or waves? • YES!

12. Erwin Schrodinger, 1925 • Quantum (wave) Mechanical Model of the Atom • Complicated equation used to estimate an e-’s location • 4 quantum numbers describe the location of e- in an atom Yikes! You DON’T need to know this!

13. Quantum Model of Atom • Quantum model of atom: • Pattern of e- arrangement in an atom, described by quantum numbers. • Quantum Numbers: • 4 numbers that describe the properties and position of an e-. • Orbital: • A region in space in which there is high probability of finding an electron.

14. Four Quantum Numbers • Principal Quantum Number = “n” • Main energy level of an e- • Angular Momentum Number = “l” • Indicates shape • Magnetic Quantum Number = “m” • Indicates oreintation • Spin Quantum Number = “spin” • Indicates direction e- is spinning

15. Principal Quantum Number: “n” • Indicates main energy levels • n = 1, 2, 3, 4…

16. Angular Momentum Number, “ℓ” • Indicates shape of orbital sublevels • ℓ = n-1 ℓ sublevel 0 s 1 p 2 d 3 f 4 g Elements in specific regions of the periodic table have similar shapes.

17. Orbital Shapes

18. Magnetic Quantum Number, ml • Indicates the orientation of the orbital in space. • Basically which spot it occupies. • Values of ml :integers -l to l • The number of values represents the number of orbitals possible. • Example: if n = 3, l= 2, ml = -2, -1, 0, +1, +2 so ml could be in any of these spaces: ___ ___ ___ ___ ___ -2, -1, 0, +1, +2 Which sublevel does this represent? Answer: d

19. Magnetic Quantum Number, ml

20. Electron Spin Quantum Number, (ms or s) • Indicates the spin of the electron (clockwise or counterclockwise). • Values of ms: +1/2, -1/2

21. Example 1: • Fill out this chart for the following quantum numbers: (3, 2, -1, -1/2)

22. Example 2: • List the values of the four quantum numbers for orbitals in the 3d sublevel. • Answer: • n=3 • l = 2 • ml = -2,-1, 0, +1, +2 • ms = +1/2, -1/2 for each pair of electrons