1. Quantum Mechanics

2. Objectives
Understand the problems with electromagnetic theory that lead to the development of quantum mechanics.
Be able to calculate the energy of a photon.
Be able to calculate the KE of an ejected electron in the “photoelectric effect.”

3. Blackbody Radiation
James Maxwell’s e/m wave theory of light could not explain two things:
#1 Blackbody Radiation
theory ≠ observations
hot objects should emit light of all wavelengths, cooling immediately

4. Is Energy Quantized?
Max Planck said that if energy is quantized (little bundles) then the observations make sense
he showed that a finite number of l will reproduce the graph
he never truly believed that energy is quantized

5. Light Quanta
Einstein (1905): light exists as particles with distinct amounts of energy (called quanta or photons)
The energy of photon: E = h·f
h = x J·s
In joules (J) and electron-volts (eV), what is the energy of a He-Ne laser photon (l = 633 nm)?
1.00 eV = 1.60 x J

6. The Photoelectric Effect
The intensity of light does not determine if e- will be ejected from a metal surface
depends on color
Einstein: photons with high frequency can eject e-
KE = hf - f
dim blue light
ejects electron
bright red light
does nothing
E = hf KE
- f
“work function”

7. Photoelectric Effect Problem
Zinc has a work function (f) of 4.31 eV. If 4.74 x 1014 hz
light shines on a zinc surface, what is the kinetic energy
of the particles ejected from the surface?

8. Solar Panels
Solar panels use the photoelectric effect to convert light into current

9. Objectives
Understand the concept of Compton scattering and be able to calculate the momentum of a photon.
Understand the concept of deBroglie waves and be able to calculate the wavelength of a subatomic particle (or any other object with momentum).

10. Quantum Mechanics
Energy is quantized; it exists in little bundles (quanta).
quantum mechanics:
the study of mechanics at the subatomic level

11. Waves acting like particles: Compton Scattering
PROOF
E = hf and f = c/l
E = hc/l E = mc2
mc2 = hc/l
mc = h/l
p = h/l
deflected particle has gained momentum
X-ray
X-ray with less
momentum
Arthur Compton (1922): e/m waves have momentum that can be transferred in “collisions”
Photon momentum: p = h / l
X-rays have high p and can annihilate DNA.

12. Photon Momentum Calculation
What is the momentum of an X-ray with a wavelength of nm?
p = h / l
If the X-ray could transfer all of this momentum to a stationary neutron in a collision, what is the resulting velocity of the neutron?

13. Particles acting like waves: De Broglie Wavelength
1923: Louis de Broglie said if waves act like particle-like properties, perhaps particles can act like waves.
de Broglie wavelength:
l = h/p or l = h/mv
Electrons should diffract and interfere in a manner similar to light.
electron diffraction pattern

14. De Broglie l Problem
A typical virus has a diameter of 100 nm, which is too small to be seen using light (light diffracts around it). At what minimum speed must electrons travel to be used to observe a typical virus (they reflect back if l ≤ 100 nm)?

15. Objectives
Understand how electron orbitals relate to constructive interference.
Be able to calculate the orbital radii of hydrogen atoms and the wavelengths (colors) produced by these atoms.

16. Niels Bohr
Niels Bohr (1913): calculated the allowed energies of the e- in an H-atom (energy levels).
He eventually thought these levels represent orbits in which an electron constructively interferes or reinforces itself.

17. The Hydrogen Atom
Bohr calculated the allowable orbital radii of the hydrogen atom:
If: l = 2p r and mv = h / l
then: mv = h / 2p r
He also postulated that an electron’s momentum is quantized…
mv = n · h / 2p r
v = n h / 2p rm
v2 = n2h2 / 4p2r2m2

18. The Hydrogen Atom
Next, Bohr said that the electric force acts as centripetal force…
Fe = Fc
kq2 / r2 = mv2 / r
r = kq2 / mv2
He replaced v2 with n2h2 / 4p2r2m2
r = kq2/m(n2h2 / 4p2r2m2)
and simplfied:
r = n2 (h2/4p2kq2m)
r = n2 (5.29 x m)
rn = n2 (52.9 pm)

19. Example Problem rn = n2 (52.9 pm)
What is the orbital radius of an electron in the 2nd energy level of a hydrogen atom?
rn = n2 (52.9 pm)

20. The Hydrogen Atom
Further algebra can determine the relative energy of each
level, which is the sum of the electron’s PE and KE:
En = –2pK2mq4/h2n2
En = – 2.17x10-18 J · (1/n2)
En = –13.6 eV · (1/n2)
Ephoton = Ef – Ei
What is the wavelength of light produced when an
electron goes from n = 4 to n = 2 in hydrogen?

21. Objectives
Understand how the Heisenberg Uncertainty Principle hints at the particle-like vs. wave-like nature of matter and energy.
Revisit the double-slit experiment with only one particle going through the slit.

22. Heisenberg Uncertainty Principle
1927: it is not possible to precisely measure both the momentum (p) and location (x) of a subatomic particle.
Dp and Dx =
uncertainty
in measured
values
particle or wave?
large Dp, small Dx: particle-like
small Dp, larger Dx : wave-like

23. The Double Slit Experiment Revisited
When Young’s double-slit experiment is performed so that only one photon reaches a slit at a time, fringes still form!
Why? Do they know where to go?
Photons have a higher probability of hitting some areas more than others.

24. Schrödinger’s Orbitals
1925:
Erwin Schrödinger calculates the shape of orbitals where
e- are most likely to be located.

25. Particle or Wave? Particles mass momentum position gravity Waves
wavelength
frequency
diffraction
interference
In the macroscopic world, these concepts seem separate, but they smear together in the microscopic world.