1. If light can have a dual nature why not matter???
Electrons don’t move at the speed of light (although in certain cases they can be close), so rearrange the equation for the mass of the photon to solve for the momentum of the electrons using “v” as the velocity of the electron
l = h/mv
m = h/cl
becomes
m = h/vl
mv = momentum
DeBroglie Eq.

2. What would the wavelength of a baseball be (142 grams) thrown at a speed of 100 miles per hour (44.4 m/s)
1.1 x m
Not a significant size compared to the space it exists in!
What would the wavelength of an electron be (9.11 x grams) whizzing about it’s orbit in the Bohr model traveling at a speed of 2.0 million meters per second?
3.6 x m
A significant size compared to the space it exists in!

3. Light waves passing through a single slit

4. Light waves passing through a double slit
Interference pattern
Light waves passing through a double slit

5. Electrons
Interference pattern

6. Randomly closing a slit…forcing the electrons to go through one slit or the other
No interference pattern

7. You get an interference pattern when you allow it to choose which slit to through…you don’t when you make it go through one slit or the other!!!
Implication:
The electron goes through both slits at the same time! Very much unlike a particle…acting as a wave. (smeared out…less discrete)

8. Only certain wavelengths work! Only certain frequencies work!
Fits
Fits
Doesn’t Fit
Only certain wavelengths work!
Only certain frequencies work!
Only certain energies work!
Therefore; energy levels exist!

9. ĤY = EY ↑energy of electron Dx • Dmv ≥ h/4p
Schrödinger: The Wave Equation
psi, the wave function↓
(locations)
(many solutions)
ĤY = EY
One Look →
mathematical operator ↑
↑energy of electron
Heisenberg:
The Uncertainty Principle
(The observer affects the observed)
can’t know both well
Future location of electron
position
Depends on
velocity
Dx • Dmv ≥ h/4p
Born:
Electrons are probability waves
(“Waves of Chance”)

10. Y2
→ describes the probability of finding the electrons in the locations described by Y
High probability region in space where the electron is likely to be found….
orbitals
(pictured as boundary surface diagrams)