VPython Demo: Scattering
alpha_on_alpha.py
Rutherford_dist.py
Rutherford_dist_pudding.py
alpha_on_electron.py
Scattering: Explain the geometry of impact parameter b and scattering angle. Show
alpha particle on a particle that is 8 proton masses (program alpha_on_alpha.py). Start
with zero impact parameter, then show b = 2e-15 m, then b = 40e-15 m. Establish that
larger impact parameter gives smaller scattering angle. Then set target to be another alpha
particle and show what happens: emphasize that the 90 degrees between the outgoing
momenta is VERY special; only for equal masses. Note that even though the collision is
elastic, during the collision the kinetic energy does decrease (as electric potential energy
increases). “Elastic” means that there is no change in internal energy from the initial state
(far away) to the final state (far away). Set target mass to 0.1 proton masses to show
again what happens when a heavy projectile interacts with a light target.
Scattering distributions: Show program Rutherford_dist.py (could hand out red-cyan
glasses and use scene.stereo = 'redcyan'). Emphasize that the distribution tells us about
the nature of the interaction.
Show program Rutherford_dist_pudding.py in which the target is a single proton.
Footnote to the main issues: Show program alpha_on_electron.py to emphasize that in
Rutherford scattering you can forget the atomic electrons, which
are swept away due to their low mass, with little effect on the
alpha trajectory. The collision occurs deep inside the atom. (If
you let the program run long enough, you see that the two
particles orbit each other; this would not happen in the more
complicated environment of a solid.) Note that this is essentially a
bowling ball hitting a ping-pong ball: the bowling ball’s velocity
hardly changes, but the ping-pong ball moves twice as fast as the
bowling ball.
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Also stress difference between nuclear scale (10–14 m) and atomic scale (10–10 m). Show
that we can ignore all but one nucleus in the scattering. At far left of blackboard draw a
dot 0.5 mm in radius to represent one gold nucleus. Have students calculate how far
away, to scale, (the next gold nucleus should be drawn. This is about 5 meters! (Factor of
about 104). Draw another tiny dot far away. The essence of the Rutherford experiment is
one alpha at a time colliding (electrically) with just one gold nucleus, and no electrons
around. Even if the 79 protons were spread apart, they too would be nearly isolated.
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