Unit I On-a-Page

Principles and Definitions

If you have had Dr. Toggerson or Dr. Bourgeois for Physics 131, you are familiar with a distinction made  between principles and definitions. The are the fundamental rules of the Universe that describe how things work. Concepts which are , on the other hand, simply describe a quantity. For example,

\vec{p} = m \vec{v}

is the definition of momentum for a massive particle; this equation offers no deep foundational insights on how the universe works. We physicists simply noted that the quantity m\vec{v} came up a lot and we gave it a name \vec{p}. In order to describe how the Universe works, principles will often involve multiple definitions. Note, sometimes a principle or definition has an equation, other times it is just stated in words! This connects to Physics Goals 1 and 2 for this course.

To help get those of you who may not be used to this distinction acquainted and to help organize the huge amount of factual information in this particular unit, I will list the principles for this unit. You can quickly see how short this list is.

Principles for this Unit

Basic Properties of Light

  • Light in a vacuum always travels at the speed of light c=299792458 \, \frac{\mathrm{m}}{\mathrm{s}}

Basic Properties of Waves

  • Fundamental connection between \lambda, \nu, and wave speed v:  v = \lambda \nu
  • The A is independent of frequency \nu

Basics of Energy

  • Energy is conserved. The change in  \Delta E is caused by the exchange of energy through Q and W:  \Delta E  = Q + W .

Wave Particle Duality

  • You can convert from the wave picture to the particle picture through the de Broglie relation:  p = \frac{h}{\lambda} where p is the momentum of the particle.
A Venn-diagram showing the different sciencesIn chemistry, you probably saw the conversion between energy and wavelength for photons done through the equation  E = \frac{hc}{\lambda} . We will NOT be considering that as a principle to begin analyses / solving problems. The reason is that, in chemistry, you only considered converting between energy and wavelength for photons. We want to think about BOTH photons AND electrons. It turns out, that  E = \frac{hc}{\lambda} ONLY works for photons, while  p = h / \lambda works for both photons and electrons! Thus we consider  p = h/\lambda to be our principle. Many students get tripped up by applying  E = \frac{hc}{\lambda} to electrons. Don’t fall into this trap!
  • The probability of finding a particle in a given location is proportional to the square of the amplitude P \propto A^2.
    • Increase amplitude by 3, probability goes up by 9.
    • For light, we represent the amplitude not by A but by E. This is NOT the energy (confusing I know, but it is what it is). We will see why we use E later in the semester.

Standing Waves

  • The wave must “fit” in the box or on the ring. For a box, this means that the box must be an integer number of 1/2 wavelengths. For a ring, an integer number of waves must fit around the ring.

Instructor’s Note

 

The ideas in this unit can be connected in many different ways. One possible useful way to organize such information is in a “concept map” like the one shown below. The map is also available at this link.

In this map:

  • UMass maroon bubbles are big ideas
  • Yellow bubbles apply to massless particles like light
  • Green bubbles apply to massive particles like electrons

I would recommend printing a copy for use in class!

A concept map of all of the ideas in Unit 1
Unit 1 on a page!

License

Icon for the Creative Commons Attribution 4.0 International License

Physics 132: What is an Electron? What is Light? by Roger Hinrichs, Paul Peter Urone, Paul Flowers, Edward J. Neth, William R. Robinson, Klaus Theopold, Richard Langley, Julianne Zedalis, John Eggebrecht, and E.F. Redish is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

Share This Book