1. Standing Waves Reminder Confined waves can interfere with their reflections Easy to see in one and two dimensions –Spring and slinky –Water surface –Membrane Examples on next slide

2. Circular membrane standing waves 2-D Standing Waves Nodes are lines Higher frequency  more nodes Source: Dan Russel’s pageDan Russel’s edge node onlydiameter nodecircular node

3. Standing Waves Reminder Confined waves can interfere with their reflections Three-dimensional examples –Sound waves –Microwave ovens

4. de Broglie’s Wild Idea Maybe electrons act as waves! After all, light can act like a particle. Momentum of a photon: p = h/ p = momentum h = Planck constant = 6.626  10 -34 J s = wavelength

5. Question If an electron and an atomic nucleus have identical speeds, which has the shorter wavelength? 1.The electron. 2.The atomic nucleus. 3.Both will have the same wavelength. 4.It depends.

6. de Broglie’s Wild Idea What is an electron’s wavelength? p = h/, so  h/p Source: Griffith

7. Waves and Uncertainty Energy known exactly, position not determined Energy less specific, position more specific Energy not determined, position known exactly

8. Heisenberg Uncertainty Principle  p = uncertainty in momentum  x= uncertainty in position h= Planck constant = 6.626  10 -34 J s  p  x  2h

9. Question The uncertainty principle tells us that A. Particles have wave-like properties. B. You cannot specify both position and momentum beyond a certain accuracy. C. Quantum physics is really wild. D. All of the above.

10. Electron Energy Levels The electrons do not collapse onto the proton because: Smaller radius  smaller  x This requires larger  p  larger energy! This is also why  -particles are ejected from the nucleus.

11. Nuclei (Aside) So… how can protons and neutrons be confined to a nucleus? Momentum p = h/, so wavelength = h/p Light, heavy objects with same have same p –mV = Mv But… a heavy object has much lower speed and much lower kinetic energy! –½ mV 2 > ½ Mv 2 So confined massive things can have lower KE

12. Quantum Wavefunctions Tell everything we know about a particle Mathematical functions of position, time Determined by particle’s energy, mass, force fields Square is probability density

13. Electron Orbitals Higher energy  more nodes Exact shapes given by four quantum numbers –n, l, m l : shape; m s : “spin” Pauli Exclusion Principle: No two electrons can have the same four quantum numbers

14. Quantum Number n n: 1 + Number of nodes in orbital Sets energy level Values: 1, 2, 3, … Higher n → more nodes → higher energy

15. Quantum Number l l: angular momentum Number of angular nodes Values: 0, 1, …, n−1 Sub-shell or orbital type l0123l0123 orbital type s p d f

16. Quantum number m l Orientation of angular momentum Values: −l,…, 0, …, +l Tells which specific orbital (2l + 1 of them) in the sub-shell l0123l0123 orbital type s p d f degeneracy 1 3 5 7

17. Quantum Number m s Spin direction of the electron Only two values: ± ½

18. Hydrogen Orbitals Source: Chem Connections “What’s in a Star?” http://chemistry.beloit.edu/Stars/pages/orbitals.html

19. Filling Orbitals An electron occupies the lowest-energy available orbital If only one electron, all orbitals with the same n have the same energy Electron-electron repulsion makes it more complicated for multi-electron atoms –Then s < p < d < f

20. Fill Orbitals Do Activity 1: Quantum #s (pp 105–107) Start n ← 1 l ← 0 m l ← 0 m s ← −1/2 m l ← m l +1 m l ← −l m s ← +1/2 l ← l+1 m l ← −l m s ← −1/2 n ← n+1 l ← 0 m l ← 0 m s ← −1/2 More ? m l < l ? m s =−1/2 ? l < n−1 ? YN Y YY NN

21. Filling Orbitals More complications with many electrons s < p < d < f for the same “energy level” n Energies of different n may cross

22. Filling Orbitals: diagonal 1s 2s2p 3s3p3d 4s4p4d4f 5s5p5d5f5g 6s6p6d6f6g6h 7s7p7d7f7g7h7i (2)(6)(10)(14)(18)(22)(26)