Quantum Mechanics 101

Waves? or Particles?

Interference of Waves and the Double Slit Experiment

Waves spreading out from two points, such as waves passing through two slits, will interfere

d

Wave crestWave troughSpot of constructive interference

Spot of destructive interference

The Double-slit experiment for particles

Particles do not diffract; they either go through a slit or they don’t

Particles passing through a slit hit a screen only in a small area; if they all have the same initial velocity, they will all hit at the exact same point

Particles passing through two slits will form two maxima in front of the two slits

What Happens if Electrons Pass Through Small Openings?

What does that tell you about electrons?

The Plot Thickens

An experiment called the “photoelectric effect” also gives

unexpected results!

The Photoelectric Effect, Pictorially

Light shining on a material may be absorbed by electrons in that material If an electron absorbs

enough energy to break free of its bonds, it can leave the material

cresttrough

The kinetic energy of the electron will be equal to the energy absorbed by the electron minus the energy needed to free it, provided the electron does not lose any energy in collisions

Wave theory predicts . . .

the energy of emitted electrons should depend on the intensity of light

electrons will need to soak up energy from wave for period of time before being ejected

the frequency of light won’t affect the maximum kinetic energy of electrons

The Photoelectric Effect, Experimentally

As a given color (frequency) of light enters the black box-like photoelectric head, it falls on a plate of electron-emitting material inside

Emitted electrons are collected on another plate nearby, producing an electric potential difference between the two plates (like a capacitor)

When the capacitor is fully charged and no more electrons can be added, the potential energy of the capacitor equals the maximum kinetic energy of the electrons trying to leave the original plate

The potential difference on the capacitor at this point is called the stopping potential Vs for the electrons, and it is proportional to the maximum kinetic energy of electrons emitted by the light:

K = eVs = Eabsorbed - Work function (energy needed to remove electron)

Do the Photoelectric Experiment

Upon what does the energy of emitted electrons appear to depend?

Experiment sees . . .

the energy of emitted electrons does not depend on the intensity of light

electrons are ejected immediately the frequency of light does affect the maximum

kinetic energy of electrons; kinetic energy is linearly dependent on frequency

intensity of light determines number of emitted electrons (photocurrent)

Einstein to the Rescue

Einstein suggested that light was emitted or absorbed in particle-like quanta, called photons, of energy, E = hf

cresttrough

If an electron absorbs one of these photons, it gets the entire hf of energy.

If that energy is larger than the work function of the metal, the electron can leave; if not, it can’t:

Kmax = Eabs – = hf -

Einstein’s Photoelectric Theory

eVs = Kmax = hf –

Kmax f Is this consistent with what you saw in the experiment?

Electrons are ejected as soon as a photon strikes the material.

Is this consistent with what you saw in the experiment?

Einstein’s Photoelectric Theory

eVs = Kmax = hf –

If hf < , no electrons are emitted; cutoff frequency

What should the slope of a K vs. f plot yield? Is that what you got?

The Conflict Wave theory accurately describes interference and

diffraction, along with other behavior of light, such as dispersion and refraction

The particle theory accurately describes photoelectric effect, black body radiation, and other experimental results

Is light a particle? Or is it a wave? Is a platypus a duck? Or is it a beaver? Am I my mother? Or am I my father?

The Resolution

Light is not either a particle or a wave Light exhibits wavelike properties when traveling Light exhibits particlelike properties when

interacting with matter deBroglie suggested that traditional “particles”,

like the electron, also exhibit wavelike properties p=h/, so large (macroscopic) momentum means

small (undetectable) wavelength

The interpretation Light and “particles” propagate through space as

probability waves I cannot say for certain where a particle is, where

it was, or how it got to wherever it might have been

I can, however, say where it is most likely to be found, where it most likely was, and how likely it is that it took a particular path

This behavior is described by a wave function (x,y) which obeys Schrödinger’s equation

More interpretation The probability of finding a particle in a particular

region within a particular time interval is found by integrating the square of the wave function:

P (x,t) = |(x,t)|2 dx = |(x)|2 dx |(x)|2 dx is called the “probability density; the

area under a curve of probability density yields the probability the particle is in that region

When a measurement is made, we say the wave function “collapses” to a point, and a particle is detected at some particular location

What have we learned today? Quantum mechanics is AWESOME, but it

challenges our physical intuition Light and “particles” behave like waves when

traveling and like particles when interacting or being observed

Since they propagate like waves, both light and “particles” can produce interference patterns

We can describe this duality through the use of a wave function (x,t) which describes the (unobserved) propagation through space and time