1. The Dawn of Quantum Theory
Chapter 1
The Dawn of Quantum Theory

2. Chapter Overview What we knew by late 1800’s Unexplainable Experiments
Angular Momentum & Kinetic Energy
Bohr H-atom & Rydberg
Wave-particle Duality – de Broglie
Two-Slit Experiment
Uncertainty Principle

3. By the Late 1800s: Chemists had: Physicists had:
Scientific Community believed:
Generated a method for determining atomic masses
Generated the periodic table based on empirical observations
Resolved the structure of benzene
Elucidated the fundamentals of chemical reactions
Generated the relationship between heat & work
Developed the first two laws of thermodynamics
Demonstrated the wavelike nature of like
Applied statistical mechanics to chemical systems
Atoms are the basic constituents of matter
Newton’s Laws are universal
All the phenomenon in the world is deterministic

4. Sounds great so what’s the problem?

5. Unexplainable Experiments
Quantum to save the day!
Black body radiation
Photoelectric effect
Discrete atomic spectra
Resolves these issues
Explains bonding, structure & reactivity
Uses probability instead of determinism
Generates rules for electrons in atoms & molecules
So what does it all mean?
Atoms are not the smallest or most microscopic objects
Something else is needed to explain these experiments

6. Blackbody
Radiation

7. Blackbody Radiation (BBR)
A heated object will turn red then white then blue as frequency increases with T
Emitted frequency depends on system composition
An ideal body aka blackbody absorbs/emits all frequencies leading to the radiation
What is it?
Classical Physics (CP)
Breakdown
BBR resulted from “antennae-like” electrons which oscillate equally at any frequency
Blackbody Radiation (BBR)
Rayleigh-Jeans Law
UV-Vis Catastrophe
Used in CP to generate relationship between spectral density, , and the frequency, 

8. Blackbody Radiation (BBR)
PLOT TWIST
Enter Planck
Planck was one of the first to cognize variables may not have a continuum of values but instead be quantized
Proposed energy of oscillating e-’s  frequency or
This ‘n’ is our first taste of quantization
Blackbody Radiation (BBR)
Reproduces RJLaw at low ’s or h << kBT
BBR by Planck

9. Photoelectric
Effect

10. Photoelectric Effect (PE)
What is it?
Classical Physics Explanation
Emission of e-’s from a metallic surface due to UV light exposure
Increasing intensity (I) will cause e- ejection
PE will occur as long as the  is high enough
Experimentally e- ejection is independent of I
Experimentally there is a threshold 
Below this threshold no e-’s are ejected
Above this threshold the kinetic E of the e-’s varies linearly with 
Photoelectric Effect (PE)

11. Photoelectric Effect (PE)
Einstein to save the day
Energy is made of packets aka photons aka quanta
Energy is proportional to light frequency
 = work function & is analogous to the ionization energy of an isolated metallic atom
recall Planck also said this
Photoelectric Effect (PE)
Once  is met the remaining energy is converted to speed
Einstein’s h is the same as the one derived by Planck

12. Discrete
Atomic
Spectra

13. Discrete Atomic Spectra
Only certain frequencies are absorbed/emitted
What is it?
Rather than the full spectrum UV/Vis
Discrete Atomic Spectra
Rydberg generalization
Balmer was the first   n-2
𝜈 = − 1 𝑛 2 𝑐 𝑚 −1 𝑛=3,4,5…
This treatment only accounts for visible portion
Now the rest are taken into consideration

14. Now that we have proven quantum is our friend let’s get to know it better

15. Angular Momentum Spinning right round
A particle rotates around a fixed point with radius r
We can write the kinetic energy, T as:
𝑇= 1 2 𝑚 𝑣 2 = 1 2 𝑚 𝑟 2 𝜔 2 = 1 2 𝐼 𝜔 2   where I is the moment of inertia
Angular Momentum
Writing T in terms of moment we get:
𝑙𝑖𝑛𝑒𝑎𝑟:  𝑇= 𝑝 2 2𝑚  𝑎𝑛𝑔𝑢𝑙𝑎𝑟: 𝑇= 𝑙 2 2𝐼

16. The H-atom
Bohr
& Rydberg

17. Bohr Hydrogen Atom (BHA)
Consists of a massive centrally located positive nucleus and a smaller negative e- which is in a fixed orbit about this nucleus
What is it?
A tale of two forces
Bohr Hydrogen Radius
Coulomb’s Law
Centrifugal Force
Bohr Hydrogen Atom (BHA)
Need for Equality
Their equality keeps e- from colliding with the nucleus
Bohr’s Assumptions
Model Limitations
Fails for multi-e- systems
Fails in presence of magnetic field
Atoms do not radiate En (n=1, 2, 3 , …) and n = 1 is the ground state and most negative
Angular momentum is quantized orbits require an integer number of de Broglie s

18. Total E, Rydberg, &  En & Rydberg Reduced Mass
Total Energy of Bohr H-atom
The potential energy e- and p+ separated by distance r is − 𝑒 2 4𝜋 𝜀 0 𝑟
Total E, Rydberg, & 
Reduced Mass

19. Wave-Particle Duality
Duality Math
Hello de Broglie!
Einstein proved: 𝜆= ℎ 𝑝
de Broglie claimed: 𝑝=𝑚𝑣
Putting them together: 𝜆= ℎ 𝑚𝑝 (de Broglie )
Wavelike: supported by classical optics
Particlelike: supported by photoelectric effect
de Broglie: if light is a wave and can act like a particle then why can’t a particle act like a wave
Wave-Particle Duality
We are all oscillating – proof by example
What is the de Broglie wavelength for a 75 kg boy and an electron both traveling at 10 mph?

20. More about de Broglie de Broglie & Bohr de Broglie in real life5
de Broglie in real life
More about de Broglie
X-ray Diffraction
Electron Microscope
Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Occurs when X-rays are fired at a crystalline substance
Results as interatomic spacing is on the order of X-ray
Uses applied voltage through an electromagnetic field
Possess a 1 nm resolution compared to light microscope which is limited to visible range (250 nm – 800 nm)
Amusing Planet – Kaushik Patowary
Used to gain insight on crystal structure for compounds

21. Two-Slit Experiments Further proof of wave-particle duality
Young’s Setup
What happens when only one particle at a time is allowed to pass?
Two-Slit Experiments
Through the Wormhole

22. Heisenberg Uncertainty Principle (HUP)
So much uncertainty
(thanks Heisenberg!)
The Math of HUP
xp  h
Heisenberg Uncertainty Principle: the exact momentum and position of an e- cannot be known simultaneously
The deltas indicate stand deviations
To see the electron we need a source on the order of visible light
As soon as we shine that light the momentum is changed
So as one gets smaller the other gets larger in order to adhere to the relationship
Heisenberg Uncertainty Principle (HUP)
http/imgur.com/gallery/dZjiW
Consequences of HUP
Bohr assumed e- is a particle with known velocity and position
In order to complete the picture we need a true wavelike description of e-’s (CHAPTER 2 PLUG)
We do not know what the velocity is if we know the e- is in the atom