Planck’s Constant and Quantum Theory – AS Physics Revision

The Constant

  • Planck’s constant relates the energy of a photon to its frequency
  • (It’s relevant to the photoelectric effect. See other post)
  • The constant is 6.63 *10^(-34)
  • It’s in units Js (not that it needs units), and it’s represented by the letter h
  • The equation is E=hf, where E is the energy of the photon, and f is the frequency
  • Photons are tiny, and don’t carry much energy
  • You need loads of photons to carry decent amounts of energy, so it makes sense that Planck’s constant is very small
  • Even rather high-frequency photons only carry small amounts of energy
  • (It’s all relative, though. To the electrons, it must seem like higher-frequency electrons are carrying an awful lot of energy)
  • Sometimes you’ll be told the power of a light source, and the frequency of photons it emits, and asked to work out how many photons it emits per second

Two other things

  • The charge on a single¬†electron is -1.6 *10^(-19)
  • This is called the elementary charge, and represented by e
  • An electron volt, eV is the energy of one electron in a potential difference of one volt

Anyway, Quantum Theory

  • It seems light isn’t a particle, or a wave – it’s more complicated than that
  • Light is clearly a particle (photons, anyone?), yet it clearly exhibits wave-like behaviours, some of which can’t be explained using the particle theory
  • The current theory is that photons take literally all possible paths they could possibly take, at once
  • They’ve got to end up somewhere, though, and the destination is all down to probability
  • (The probability of something happening given that something else has happened is different from the probability that just the first thing happens, which is probably why photons do weird things when you’re checking up on them. That doesn’t seem to be part of the course, though. But I’m sure there are plenty of good books on it)

Working Out The Probability

English: Graph of a phasor as a rotating vector

English: Graph of a phasor as a rotating vector (Photo credit: Wikipedia)

  • There are infinite paths to get from one particular place to another particular place, but, brilliantly, most of them will cancel out, because they’re symmetrical/mirror images of another path
  • As a result, you can consider only a few very simple paths, and still get a good idea of the probability of a photon arriving somewhere
  • You stick phasors on these paths and get them to rotate as they move from the start to the finish
  • At the end, you remember what directions they were all pointing in, and add them together (the same way you’d add vectors) to get a resultant phasor
  • The probability of a photon arriving in this place is proportional to the resultant phasor amplitude squared
  • The amplitude and starting direction of the phasors don’t matter, as long as they are the same for each path#
  • The places with the highest resultant phasor amplitude will be hit by the most electrons

Calculating Your Phasor Stuff

  • The time a phasor should take to rotate once is the period of the photon (one divided by its frequency)
  • The wavelength of a photon is the distance it will travel during one phasor rotation
  • The number of times the phasor will rotate along the path is the time it takes to travel the path, divided by the time it takes the phasor to rotate once, which is also the time taken to travel the path multiplied by the frequency
  • Notice how we’re still talking in terms of waves…

About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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