THE UNIVERSITY OF BRITISH COLUMBIA
Science 1
Physics Assignment # 3:
QUANTUM MECHANICS
19 Jan. 2000 - finish by 26 Jan. 2000
- 1.
- Photon Drive:
A laser generates
1
kW of power continuously
in a beam of light of wavelength
nm.
The beam uniformly illuminates a circular spot
1
cm in radius.
- (a)
- How many photons does the beam contain per unit volume?
- (b)
- What is the momentum of a single photon in the beam?
- (c)
- If the beam is completely absorbed by a blackbody,
what thrust (force) does it exert on the blackbody?
plus
Tipler Ch. 25, problems 26, 35, 38 & 51;
. . . and
Tipler Ch. 26, problems 8, 10, 12 & 13.
JUST FOR FUN: Guns vs. Lasers -
Somewhere in deep space
a battle is being fought between two adversaries
1,000
km apart.
One side has an ultraviolet laser cannon that ``shoots'' a beam of
10.204
eV photons through a circular aperture of diameter a = 2 mm.
The other side is using an ``ideal rifle'' in which
individual lead atoms are used as ``bullets.''
These atoms are prepared in a plane wave state where their positions
are completely uncertain but their velocity
(v = 5000 m/s) and direction
are precisely determined; these bullets are then ``collimated'' through a
2
mm diameter hole in a steel plate.
[Treat the bullets as ideal point particles.]
Each weapon has just enough beam power to burn a 10 cm hole
in the adversary's hull in 1 s at close range.
- 1.
- Using the Rayleigh formula
for the angle
of the first minimum of the diffraction pattern
from light of wavelength
passing through a circular aperture of diameter a,
calculate the diameter of the laser beam at its ``target''
(twice the distance from the central maximum
to the first minimum).
- 2.
- Convert Rayleigh's criterion into an
uncertainty relation between
the uncertainty
in the transverse momentum of the photons
and the uncertainty
in their transverse position at the ``muzzle'' of the cannon.
Compare the result with the standard form
and briefly discuss any differences.
- 3.
- How good a marksman can one be with the ``ideal rifle?''
I.e., what will the ``pattern'' of holes
in the target look like? Sketch of the distribution
of ``hit'' positions, including scale.
- 4.
- If you were unfortunate enough to be caught in
such a battle, which weapon would you choose?
Explain your reasoning.
Jess H. Brewer
2000-01-19