Macroscopic Quanta

This project must be done by individuals.

You have read that photons are quanta of light, with energy according to

             E  =  h * v

where h is Planck's constant and v is the frequency of the photon. You've also heard that quanta are so small that one can't distinguish them on macroscopic scales.... but is that really true?

A really high-energy photon ought to have macroscopic consequences. Fill in the table below.


                                 frequency          wavelength
                                   (Hz)                 (m)
----------------------------------------------------------------------

A single photon with the
kinetic energy of a Randy 
Johnson fastball would have ...


----------------------------------------------------------------------

A single photon with the
momentum of a Randy Johnson
fastball would have ...

----------------------------------------------------------------------

Can humans create photons with the same amount of energy as a fastball? One of the biggest particle accelerators in the world is the Tevatron at Fermilab. Answer the following questions:

What is the maximum energy a proton has after it has been accelerated in the Tevatron?
What fraction of that energy is kinetic energy?
If a proton and an anti-proton at that energy collide, and turn into a single photon, how much energy does it have?
Is that as much as the kinetic energy of a fastball? If not, what fraction of a fastball's kinetic energy does it have?

Maybe the universe can create photons with more energy. There are several telescopes currently operating which look (indirectly) for gamma rays of extremely high energies. One of them is the Whipple Observatory gamma-ray telescope.

What is the diameter of this telescope?
In 2001, a paper was published in the Astrophysical Journal describing observations of gamma rays from Markarian 421. The first author is Krennrich. Find this paper, and print out Figure 2. You might check The ApJ home page.
```
          http://www.journals.uchicago.edu/ApJ/index.html
 
```
What was the energy of the most energetic photon(s) from Mrk 421 shown in this Figure?
How does its energy compare to the kinetic energy of a fastball?
Use the Figure to calculate the number of photons of this highest energy which were detected every hour with the Whipple Telescope.