Goal:
· To investigate Rutherford Scattering using the CUPS Rutherford Scattering Modern Physics software for an exactly inverse-square Coulomb force.
· To determine the effects of beam width, energy, and orientation on the scattering pattern.
References:
Beiser, Arthur. Concepts of Modern Physics 4th edition. New York: McGraw Hill, 1987.
pp. 119-129.
Ohanian, Hans C. Modern Physics. Englewood Cliffs: Prentice Hall, 1987. pp. 150-154.
Background:
The original experiment was performed in 1911 by Geiger and Marsdan. An alpha source is placed behind a lead shield. Alpha particles traveling through a hole in the lead shield approach a gold nucleus and are deflected through an angle and strike a zinc sulfide screen which emits a flash of light. By keeping track of the distribution of 's we can inquire into the nature of the atom.
alpha
source
incident path of alpha particle
alpha particles scattering distribution
b distance from incoming path
gold nucleus
(part of foil)
lead shield
screen
Pre Lab:
1. What purpose does the lead shield serve?
2. Calculate the force between the alpha particle and the gold nucleus?
3. Calculate the potential energy of the alpha particle / gold nucleus system?
Procedure:
1. Start the CUPS Modern Physics Rutherford Scattering program. From the mode menu select Single Scatter. From the force menu select 1/r2 exact.
2. Select Beam Parameters from the menu. What should the charge on the beam particles be? (notice that the scattering particle (the gold nucleus) as a "charge" of 1) Enter an appropriate value.
3. How should the width of the beam (the size of the opening in the lead plate) affect the distribution of scattered alpha particles. Design and carry out a method for checking your hypothesis.
4. How should the Beam Energy (KE right?) affect the distribution. Design and carry out a method for checking your hypothesis.
5. How should the Beam Orientation (the angle that the nucleus is rotated) affect the distribution? (remember the circular symmetry of the nucleus)
Determine a fit for N(), keep in mind zeros and assume r is the radius of the nucleus. Use the plot menu to test your ideas.
Final Discussion:
The distribution for is (see the references at the beginning of the paper):
Rutherford Scattering Formula:
where N() is number of alpha particles per area, Ni is the total number of alpha particles interacting with the gold nucleus, n is the number of foil atoms per unit volume, t is the thickness of the foil, Z is the atomic number of gold (79), e is the charge on the electron, r is the nuclear radius, K is the KE of the incoming alpha particles and is the scattering angle.
Try fitting an 1/ sin4 to the distribution in the computer program. Vary the frequency until the fit matches. Does the placement of KE make sense in the formula? n? t? Z? r?
This lab written by Michael Ventura and Brian Northcutt (c/o 1996)
