Quantum Madness

M. Rocha

Physics 2B

Fasten your mind and make sure you don't loose it when we encounter quantum junctions

The first hints of a quantized world

Plank's solution to the ultraviolet catastrophe (1900): the only way to explain blackbody radiation is by assuming that EM radiation energy is emitted in discrete chunks

E = h f = h \frac{c}{\lambda}

h = \mathrm{Planck's \ Constant} = 4.14 \times 10^{-15} eV \cdot s

The first hints of a quantized world

Einsteins's solution to the Photoelectric Effect (1905): Light itself must be quantized in order to explain why

3. Brightness affects the number of electrons emitted but not the electron's energy

Light must be particles (photons) with Energy = h f

1. The effect is easy to observe with violet or ultraviolet light but not with red light (no matter the intensity/brightens)

2. The electron's energy depends on the frequency of light.

The first hints of a quantized world

The Bohr model of the atom (1913): In order to explain the emission and absorption lines of atoms, the orbits of electrons must be restricted to discrete energy levels

The energy of the emmited/absorved photons corresponds to the energy difference between energy levels

Plank's, Einstein's and Bohr's explanations of light and atomic phenomena via quantization were a paradigm shift, and left the world very puzzled with a lot of unanswered questions

Classical picture: smooth and continuous

Quantum picture: discrete and very blurry as of 1915

If light is made out of photons (particles) how do you explain diffraction?

We relied on the wave properties of light to explain diffraction!

Double Slit Diffraction with Bullets?

Nope!

If light is made out of photons (particles) how you explain diffraction?

Diffraction occurs even on a photo by photon basis!

However if you were to close one slit the diffraction pattern does not occur!

Double Slit Diffraction with Electrons?

Double slit diffraction occurs with electrons as well!

First evidence that electrons can behave as waves as well as particles

The Wave-Particle Duality

In order to explain the double slit experiments, both electrons and photons must have wave properties in an individual basis

A photon/electron behaves as a particle when it is being emitted by an atom or absorbed by photographic film or detector, and behaves as a wave in traveling from a source to the place where it is detected

The Wave-Particle Duality

Matter Waves

If matter particles behave like waves, then they must have a wavelength. In 1924 Louis de Broglie found that the wavelength of matter is given by Plank's constant divided by the momentum of the particle

\mathrm{Wavelength} = \frac{h}{\mathrm{Momentum}} = \frac{h}{mv}

Wavelength of matter waves

Checkpoint 1

What is the wavelength of a bullet of mass 0.02 kg traveling at 330 m/s ?

h = 6.63 \times 10^{-34} J \ s \\ 1 \ J = 1 \ kg \ (m/s)^2

\lambda = \frac{6.6 \times 10^{-34} J \ s}{(0.02 \ kg)(330 \ m/s)} = \frac{6.6 \times 10^{-34} kg \ (m/s)^2 \ s}{(0.02 \ kg)(330 \ m/s)} = 10^{-34}m

\lambda = \frac{h}{mv}

For comparison, the diameter of a hydrogen atom is 10^-10 m. The wavelength of a bullet is so small than diffraction effects are not measurable

The wavelength of an electron traveling at 2% the speed of light is about 10^-10 m. The electron's diffraction effects are measurable

Explanation of Quantized Energy Levels

Electrons can only be at discrete energy levels (orbit radius), because the circumference of their orbit has to be an integer number of their wavelength in order to form standing waves, otherwise the experience destructive interference