Quantum Mechanics

1. Quantum Mechanics A way to describe electron behavior

2. The Electromagnetic Spectrum V I B G Y O R …describes the wave nature of light

3. c =  f All electromagnetic waves can be described by the equation: c = speed of light = 3.0 x 108 m/s  (wavelength) is inversely proportional to f(frequency) As wavelength increases, frequency decreases

4. Wave Comparison Red Light nm = 1 x 10-9 m • Low frequency • Long wavelength Violet Light • High frequency • Short wavelength emission

5. Electron Energy as a Wave • All of our understanding of electrons comes from radiant energy (light) they emit. • All light can be described as • particles (photons) • or as • waves (electromagnetic radiation)

7. Max Planck E studied the wavelengths of emitted by electrons… and related their frequency to the energy difference between shells. E = hf (Energy difference) = (Planck’s constant) x (frequency)

8. The electrons lose (release) energy …and they fall back to their ground state; the lost energy takes the form of light, which we study.

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10. Spectral Lines When electrons “jump” from a higher shell to a lower shell, they emit light. All of the “jumps” that occur in an atom of on element result in a signature EMISSION SPECTRUM. …for that element. Below is Mercury’s spectrum:

11. “Where” are the electrons? Like Bohr said, electrons are found in shells…(“energy levels”) …but all shells contain subshells… …all subshells contain orbitals… …and every orbital contains two electrons.

12. to make a long story short… Niels BohrAlbert EinsteinWerner HeisenbergWolfgang PauliLouis de BroglieMax PlanckErwin Schrödingerand others… …described electrons’ location and behavior by developing: Quantum Mechanical Theory “the new physics”

13. Schrodingerproposed4 Quantum Numbersto describe the location of an electron n the Primary Quantum Number l the Secondary Quantum Number m1 the Magnetic Quantum Number ms the Spin Quantum Number

14. n the Primary Quantum Number • the energy level (shell) of the electron. • the average distance from the nucleus. • n can be 1 through 7 . • there can only be 2n2 electrons in a shell.

15. l the Secondary Quantum Number • the subshell (“sublevel”) of the electron • each shell has n subshells. • Names of subshells: s (l = 0) p (l = 1) d (l = 2) f (l = 3)

16. “Where” are the electrons? Like Bohr said, electrons are found in shells…(“energy levels”) …but all shells contain subshells… …all subshells contain orbitals… …and every orbital contains two electrons.

17. m1 the Magnetic Quantum Number • tells you which orbital the electron is in. • each orbital has a specific shape. • Shapes correspond to probability of finding an electron in that area. • each orbital can hold 2 electrons. each subshell has a different number of orbitals! There is only one orbital in an s subshell. s orbitals are spherical.

18. orbitals of the p subshell: • only start at the second shell (n=2) • there are 3 orbitals in the p subshell. • they have different orientations px orbital py orbital pz orbital m1 = -1 m1 = 0 m1 = +1

19. orbitals of the d subshell: • only start at the third shell (n=3) • there are 5 orbitals in the d subshell.

20. orbitals of the f subshell: • only start at the fourth shell (n=4) • there are 7 orbitals in the f subshell.

21. “Where” are the electrons? Like Bohr said, electrons are found in shells…(“energy levels”) …but all shells contain subshells… …all subshells contain orbitals… …and every orbital contains two electrons.

22. ms the Spin Quantum Number • the last quantum number describes spin • Remember; only 2 e- per orbital • the 2 electrons in an orbital will always have opposite spins. ms ( “spin” ) can only be + ½ or – ½

23. How many electrons in each subshell? • s = 1 orbital  2 e- • p = 3 orbitals  6 e- • d = 5 orbitals  10 e- • f = 7 orbitals  14 e- Well, there are only 2 electrons allowed per orbital, so:

24. Summary # of orbitals Max electrons Starts at energy level s 1 2 1 p 3 6 2 5 10 3 d 7 14 4 f

25. Remember… Each shell has n subshells; So… the n = 1 shell only has one subshell: (an “s”) the n = 2 shell has two subshells: (an “s” and a “p”) the n = 3 shell has three subshells: (an “s” and a “p” and a “d")

26. Electron Diagrams Each arrow represents an electron. Arrow direction indicates spin. Fill from the inside out, just like Bohr Model diagrams Example: Cr 3d 3p 4s 3s 2p 2s 1s “Hund’s Rule”; one e- in each orbital before pairing Cr 1s22s22p63s23p64s23d4 Cr [Ar] 4s23d4

27. Writing Electron Configurations: 2p4 Number of electrons in that subshell Energy Level n Subshell (s, p, d or f) 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14…etc.

28. Some subshells overlap: So, we fill in this order: 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 1s2

29. Orbitals and the Periodic Table s orbitals d orbitals p orbitals f orbitals

30. The secret of periodicity:

31. 7p 6d 5f 7s 6p 5d 6s 4f 5p 4d 5s 4p 3d 4s 3p Increasing energy 3s 2p 2s 1s Electron Configuration Diagram for Phosphorous

32. Fill from the bottom up following the arrows 7s 7p 7d 7f 6s 6p 6d 6f • 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 7s2 5f14 6d10 7p6 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s • 108 electrons

33. Let’s Try It! • Write the electron configuration for the following elements: • He • Li • N • Ne • K • Zn

34. Shorthand Notation • Chlorine Longhand is 1s2 2s2 2p6 3s2 3p5 You can abbreviate the first 10 electrons with [Ne] (replaces 1s2 2s2 2p6) The next energy level after Neon is 3 So you start at level 3 and finish by adding 7 more electrons to bring the total to 17 • [Ne] 3s2 3p5

35. Shorthand Notation • Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ]. • Step 2: Find where to resume by finding the next energy level. • Step 3: Resume the configuration until it’s finished.

36. Practice Shorthand Notation • Write the shorthand notation for each of the following atoms: Cl K Ca I Bi