1. Quantum Mechanics
the world is weird

2. Rutherford’s Experiment
most
Source: Griffith

3. Atomic Emission Spectra
Source: Griffith
Emission Spectrum of Hydrogen
Why not continuous?
More spectra at

4. Bohr Model Only certain energy levels are allowed
Emits light only when electron changes energy level
Source: Griffith

5. Bohr’s model Fits H perfectly Also works for “H-like” ions
Strictly wrong, but important in development of QM
Helps us to see how QM ideas evolve

6. Bohr’s Postulate Electron angular momentum is quantized L = nh
h = h/2p
pronounced “h bar”

7. de Broglie’s Wild Idea Maybe electrons act as waves!
Standing waves can have only specific wavelengths—could something like this explain line spectra?

8. de Broglie’s Wild Idea Can electrons act as waves?
Light can act as a particle.
Momentum of a photon:
p = h/l
p = momentum
h = Planck constant =  J s
l = wavelength

9. de Broglie’s Wild Idea What is an electron’s wavelength? p = h/l
solve for l
l = h/p

10. Electrons: de Broglie and Bohr
nl = 2pr
nh/p = 2pr
nh/(2p) = rp
This is the Bohr condition that angular momentum is quantized in increments of h/(2p).

11. Explains Bohr’s Quantization
standing waves nl = 2pr
Source: Griffith

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

13. Heisenberg Uncertainty Principle
Dp Dx  h/2
Dp = uncertainty in momentum
Dx = uncertainty in position
h = h/2p =  J s

14. 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 these.

15. Electron Energy Levels
The electrons do not collapse onto the proton because:
Smaller radius  smaller Dx, l
This requires higher f, Dp  higher energy!

16. Circular membrane standing waves
Describing Electrons
Electrons are standing waves!
Circular membrane standing waves
edge node only
diameter node
circular node
Source: Dan Russel’s page
Higher energy  more nodes

17. Experimental Verification
Electrons and neutrons diffract.
Diffraction patterns match l = h/p.

18. Waves and Quantization
Boundary conditions allow only certain wavelengths to be sustained

19. Born Interpretation What is a matter wave?
Square of amplitude |Y|2 is probability density
if Y is normalized to |Y|2dV = 1
Probability of being in region dV is ∫|Y|2dV
Still detected as particles

20. What is Y? “Wave function” Everything we “know” about a particle
Function of space and time Y(r,t)

21. Electron Orbitals
Electrons’ position and energy described as standing waves!
Higher energy  more nodes
Exact shapes given by four quantum numbers
No two electrons can have the same four quantum numbers

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

23. Chemistry in Five Minutes
Molecules
Chemistry in Five Minutes

24. Covalent Bonding Electrons shared more space Electrons not shared
lower energy longer wavelength

25. Dipole-Dipole Forces Some molecules have permanent dipoles… + -
…and attract each other like bar magnets! + -

26. Charge-Fluctuation Forces
All molecules have fluctuating dipoles…
…and attract each other when their electrons move in synchrony.

27. Summary
Atoms comprise massive, positively-charged nuclei surrounded by light, negatively-charged electrons.
The uncertainty principle prevents atoms and molecules from collapsing.
Atomic and molecular behavior is described by wavefunctions.

28. Summary Electrons in atoms can have only specific energies.
Chemistry is governed by electrical forces and quantum uncertainty.