Physics 214b-2008 Walter F. Smith Assignment 4

Due: 4 pm Wednesday 2-20-08

Reading: 3.1 to 3.2

Exercises

All problems are group problems, unless otherwise marked; you are encouraged to work in small groups on these.. For the individual problems, you are not allowed to consult any other students, but you may ask me for help.

4A. We discussed in class how particle-antiparticle pairs can be created temporarily out of nothingness. Assume an electron–positron pair is created in this way. What is the maximum amount of time the pair could exist? How far would a photon move during this time?

4B. (corrected version of Townsend problem 2.24) Lasers can now be designed to emit extraordinarily brief pulses of light, down to about 100 fs. (1 fs = 1 femtosecond = 10^-15 s).

a) If one could take a snapshot of this pulse as it scattered off chalkdust sprinkled in the laser beam (something you should never do, since it messes up the mirrors and lenses), how long (in meters) would the pulse be?

b) Estimate the uncertainty in the momentum of a photon in such a pulse.

c) Show that . (This is true for light or massive particles.)

d) Estimate the uncertainty in the wavelength of the photon, assuming the nominal wavelength is 800 nm.

Townsend 2.23, 2.28 (individual problem), 2.32, 2.34 (individual problem), 2.35 (individual problem)