1. Chemistry 141 Wednesday, November 1, 2017 Lecture 24
Chemistry 11 - Lecture 11
9/30/2009
Chemistry 141
Wednesday, November 1, 2017
Lecture 24
Matter Waves and the H Atom

2. The Balmer Series n n (Hz) l (nm) 3 4.5711014 656.3
Johann Balmer worked out that the frequencies of the light emitted by excited H-atoms satisfy the equation below
n n (Hz) l (nm)    
For n = 3, 4, 5, …
where n2 > n1
RH = ×107 m-1 (Rydberg’s constant)

3. The Bohr atom
Bohr postulated that electrons traveled in circular orbits
Only orbits with certain radii were allowed
n can only be an integer!!
The energy of an electron in a given orbit is:
E depends on n
Energy is also quantized
Note that E is negative!

4. Atomic energy levels Energy levels are like a staircase
A change from lower to higher energy level corresponds to absorption of energy
A change from higher to lower energy level corresponds to emission of energy
E=0
energy of level
n=4
energy to move between levels
energy
n=3
“excited states”
n=2
n=1
“ground state”

5. Bohr atom energies Brackett Paschen Energy Balmer Lyman Energy n = 
-13.6 eV
n = 5
n = 6
Lyman
-3.40 eV
-1.51 eV
-0.85 eV
-0.54 eV
-0.38 eV
0 eV
Balmer
Paschen
Brackett
Energy
Bohr atom energies
Energy
1 eV = 1 electron volt
= 1.60210-19 J

6. Example
What is the wavelength of the photon absorbed when going from the n=2 energy level to the n=4 energy level?

7. Bohr atom: does it work? What next?
Made accurate predictions for H and He+ line spectra
Theoretical basis of Bohr’s model is questionable
There is no physical explanation for why the electron “orbits” are stable
Bohr simply threw in idea of “allowed orbits” to classical physics to get agreement with experiments
Only works for one-electron atoms
Predictions for multielectron atoms were incorrect
What next?

8. Standing wave animation
Standing waves
Node
The wave must fit inside the confined region
There must be an even number of half wavelengths: •
n =1, 2, 3, …
Standing wave animation x
More standing waves
Length

9. de Broglie’s great leap
de Broglie (1923): Could electrons behave like standing waves?
l=h/mv
m = mass of particle
λ = wavelength
v = velocity of particle
For particles
(matter)

10. de Broglie wavelength of an electron
What is the wavelength of an electron with a velocity of 3×106 m/s (me = ×10-31 kg)?
Compare this with the radius of the hydrogen atom (r = 5×10-11 m).

11. Diffraction of waves
When a wave passes through an aperture about the same size as its wavelength or smaller, it exhibits diffraction
wave appears to ‘bend’ around edges of aperture
particles that don’t hit wall pass through aperture in a straight line

12. interference of water waves
Interference of Waves
Constructive vs. Destructive
interference of water waves + =
in phase out of phase
Image from:

13. Diffraction and Interference of Light
Young’s experiment demonstrates the wavelike nature of light
A light beam passes through two slits, creating two light sources
The waves from the two sources interfere with one another
This creates an interference or diffraction pattern on the screen
Interference is evidence of wave behavior
Figure taken from:

14. Electron diffraction X-rays Electrons
Davisson and Germer first observed diffraction of electrons fired at a nickel crystal (an ordered array of atoms)
George Thomson (J.J. Thomson’s son) fired electrons at a thin piece of metallic foil
Davisson and Thomson shared the Nobel prize in physics in 1937
Amazingly, J.J. Thomson received the Nobel prize for demonstrating that the electron is a particle, while his son received the Nobel prize for demonstrating that the electron acts as a wave!
“Lucky accident” because they were initially firing the electrons at an amorphous sample of nickel, but a bottle of liquid air exploded, breaking open the sample chamber and causing the nickel surface to be oxidized by the air rushing onto the heated surface. To remove the oxide, they heated the nickel at high temperatures for a long time, this is called “annealing” and not only removes the oxide layer, but also causes large crystals to form, as opposed to having many small crystals. When they looked at this sample, they obtained something resembling a diffraction pattern, then they optimized this to get a clean diffraction pattern.

15. Matter Waves
Scientists at IBM accidentally observed standing waves from the interference of electrons on a copper surface with defect sites
They then decided to intentionally create electron standing waves by arranging iron atoms in a ring, thereby confining the space the electrons can roam in, and forming standing waves
Images from:

16. Wavelengths of larger ‘particles’
What is the wavelength of a baseball (mass = kg) moving at a velocity 18 m/s?

17. What does it all mean?
Light and matter both exhibit characteristics of both waves and particles
Large pieces of matter exhibit mostly particle-like behavior
Small pieces of matter (electrons) exhibit both particle and wave behavior
Vanishingly small pieces of matter (photons) exhibit mainly wave-like behavior
Matter and energy are not distinct – energy is a form of matter (or is it the other way around?!)

18. A very deep question:
Waves do not have a location. If a small particle (i.e. an electron) behaves like a wave, can we specify its location?

19. Heisenberg’s Uncertainty Principle
The Uncertainty Principle (Heisenberg, 1927) states:
There is an inherent uncertainty in our ability to specify an electron’s exact location
there is a fundamental limit to our ability to describe the properties of particles that are very small
Instead of certainty, we must rely on probabilities to tell us the likely location of these small particles

20. When does the uncertainty principle matter?
What is the uncertainty in the position of an electron (mass = 9.11x10-31 kg) moving with a speed of 5x106 m/s? Assume the uncertainty in the speed is 1%.