Quantum Mechanics 101 Waves? or Particles? Interference of Waves and the Double Slit Experiment Waves spreading out from two points, such as waves.
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Interference of Waves and the Double Slit Experiment
Waves spreading out from two points, such as waves passing through two slits, will interfere
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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
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)
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
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