Scattering and Structure Exploration
The purpose of this exploration is to investigate the effect of the shape of the nucleus on the
scattering of particles fired at the nucleus. Physics deals a lot with entities that are too small
or impossible to see; therefore, our knowledge must depend on indirect observations such as
scattering patterns. As you work through this exercise, have the applet open in a separate
window (if necessary click on the link, other_nuclei.swf). If you need help understanding the
simulation and variables, see the Help menu for assistance.
Rutherford Nucleus
Run the simulation by clicking “Auto-fire” and watch until the scattering pattern becomes
clear.
1. Describe the scattering pattern in words and with a simple diagram showing only the
tracks of the scattered particles.
2. Why is there no direct contact between the alpha particle and the nucleus in this
simulation?
3. According to modern theory, why does the alpha particle experience a force in the
vicinity of the nucleus?
4. Using an estimate of the distance of closest approach, determine the magnitude of the
nuclear electric field at the closest distance. Include a diagram with electric field
vectors.
5. In Rutherford’s experiments, only a few alpha particles were strongly deflected
through large angles (>90o). Why is this not happening in this simulation?
Physical Models
The simulations listed below are simplified models in which electric charges are ignored and
the scattering is due to collisions between two solid objects, like a ball against a wall. You
can choose different shapes for the nucleus in the Options menu. The main objective is to
illustrate how the shape of the object (representing a nucleus) affects the scattering pattern of
particles fired at it.
For each of the following simulations:
 Run the simulation by clicking “Auto-fire” and watch until the scattering pattern
becomes clear. You can start and stop this simulation multiple times without clearing
tracks if necessary. You can also “Fire” individual particles at various impact
parameters.
 Imagine that you have a circular scintillation screen (as in Rutherford’s experiment)
and you obtain scintillation rates for various angles around the sample containing the
particular nuclear model.
Circle Nucleus
6. Describe the scattering pattern in words and with a simple diagram, showing only the
tracks of the scattered particles.
7. Compare this pattern with the one obtained for the Rutherford Nucleus (#1). Describe
any similarities and differences.
8. Predict the relative scintillation rates—in general terms such as high, low, very high,
etc. —for the following angles: 0o, low angles (<90o), large angles (>90o) and at
180o?
9. If the circle nucleus was not visible, suggest a method to estimate its size.
10. Does the scattering pattern you obtained have to correspond to a circle? What other
shapes could give the same pattern?
Hourglass Nucleus
11. Describe the scattering pattern in words and with a simple diagram, showing only the
tracks of the scattered particles.
12. Are there any similarities with the pattern obtained for the Rutherford Nucleus (#1) or
the experimental results of the Rutherford experiment?
13. Predict the relative scintillation rates—in general terms such as high, low, very high,
etc.—for various angles, or ranges of angles, from 0o to 180o. You can use the
protractor to estimate some angles of scattering.
Square Nucleus
The square can be rotated using the angle of rotation slider. Starting at 0o, view the scattering
at a number of angles to get a sense of the change in scattering pattern.
14. In general, how does the scattering pattern change when the square is rotated to
different angles from 0o to 90o?
15. What pairs of angles would produce the same scattering pattern?
16. If the square nucleus were slowly and continuously rotating, what scattering pattern
would you expect? Try this with the simulation.
Plate Nucleus
Starting at 0o, view the scattering at a number of angles to get a sense of the change in
scattering pattern.
17. In general, how does the scattering pattern change when the plate is rotated to
different angles from 0o to 180o?
18. Describe some similarities and differences between the scattering pattern for the plate
compared with the square nucleus. You can open a second window, run the same
applet and compare the two simulations.
Unknown Nucleus
This choice from the Options menu presents an unknown nuclear model hidden behind the
question mark. Your task is to obtain a scattering pattern and identify the unknown shape
plus your reasoning.
General Instructions:
Note: Do not click “Hide” until you are finished with the unknown model.
a. Click the “Auto-fire” button and stop when the pattern becomes clear. You can
also “Fire” individual particles at various impact parameters.
b. Based on your observations of the scattering pattern, what is the hidden shape?
State your reasons.
c. Click the “Reveal” button and evaluate your prediction.
d. Click the “Hide” to start again with a different unknown.
e. Repeat this procedure, a to d, several times.
Significance of Scattering Experiments
When Geiger and Marsden performed Rutherford’s famous scattering (or gold-foil)
experiment, they observed the scattering pattern of alpha particle scintillations at various
angles; they could not see what was happening at an atomic level. However, from the
analysis of the scattering pattern and knowledge of the electric force, Rutherford was able to
determine the position, density, and size of the positive charge with the atom. Today,
physicists apply this same technique in different situations. For example, by firing electrons
at individual protons and analyzing the scattering pattern, physicists have determined that the
proton appears to consist of three smaller particles called quarks, each with fractional
elementary charges, +2/3e, +2/3e and -1/3e.