1. Phy 102: Fundamentals of Physics II
Chapter 32: The Atom & the Quantum
Lecture Notes

2. Albert Einstein ( )
Nobel Prize winner and most prominent physicist of the 20th century
Studies led to the development of whole sub-fields of physics including
Relativistic physics
Solid-state physics
Low-temperature physics
Quantum physics
Published paper describing the “photo-electric effect” in 1905
Demonstrated that light interacts with matter as photons not waves
Laid the groundwork for the quantum theory of light
Offered critical guidance to de Broglie with his “wave theory of the electron”

3. History of Quantum Theory
1900: Planck proposes that the energy of radiated light is proportional & introduced the idea of the “quantum”
1905: Einstein publishes paper of photo-electric effect, supporting Planck’s quantum hypothesis
1911: Rutherford proposes “nuclear” model of the atom
1913: Bohr proposes “planetary” model of the hydrogen atom
1924: de Broglie publishes doctoral thesis proposing wave-particle duality of matter
1926: Schrodinger develops wave equation for hydrogen atom
1926 to present: Physicists & philosophers debate the meaning of Quantum Theory

4. The Atom (just a reminder)
Two important regions
The nucleus
Represent most of the mass of the atom
Consists of protons (positive charge) and neutrons
Determines the identity of the atom (element)
The electron cloud
Represents the volume of the atom
Consists of electrons (negative charge)
Determines the chemical properties of the atom

5. The Bohr Model Ephoton = Ehigh - Elow
Planetary model of the hydrogen atom
Model explains the spectra for hydrogen
Electron orbits nucleus held in place by electrical attraction between electron and protons
When electron is “excited”
It absorbs energy (exactly equal to the energy difference between the higher and lower states of the transition)
“jumps” to a higher energy level (larger orbit)
When electron “relaxes”
It drops back to lower energy level
Releases energy in the form of a photon
The energy of the photon is exactly the amount equal to the energy difference between the the energy levels of the transition:
Ephoton = Ehigh - Elow

6. Ephoton = hf or Ephoton = hc/l
Energy & the Photon
A photon is a quantum (or single packet) of electromagnetic energy
All photons travel at the same speed in a vacuum (through empty space)
The speed of a photon (in vacuum) is
Equal to 3x108 m/s: vphoton = c = 3x108 m/s
Equal to the product of the wavelength (l) times the frequency (f) of the photon: c = l.f = 3x108 m/s
The energy of a photon is
Proportional to the frequency: Ephoton ~ f
Inversely proportional to the wavelength: Ephoton~ 1/l
To calculate the energy of a photon:
Ephoton = hf or Ephoton = hc/l
{where h is planck’s constant, h = 6.63x10-34 J.s}

7. Wave Model of the atom
Electrons orbiting the nucleus of an atom exist as “standing waves”
They exist as “cloud” and are not actually “particles”
The cloud is the “standing wave” (which just means that it is self reinforcing and thus stable in that state)
The electron waves are described by Schrodinger’s equation
Electrons are described by a wave function, y
The square of the wave function, y2, represents the “probability density function” (or, probability per unit volume of finding the electron at any particular position at a particular time)
According to Schrodinger’s equation
there are a certain number of allowed states the electron can have
The organization and geometry of the allowed states ultimately defines the properties of an atom’s electrons & the structure of the periodic table