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LAB: Rolling with Rutherford
Background: In 1908 Ernest Rutherford performed an
experiment where he bombarded a thin gold foil with alpha
particles. An alpha particle is a radioactive particle that has
a mass of 4 and a positive charge. The purpose of this
experiment was to try to determine the structure of an atom.
The common theory of atomic structure prior to Rutherford’s
experiment was that atoms were a mixture of protons and
electrons uniformly distributed (like a chocolate chip
cookie). The expected result was that the alpha particles
would pass through the foil, or be partially deflected
(bounce back or off). This in fact was true for 99% of the
particles. However, one particle in 8000 did not follow this pattern – some alpha particles hit the zinc sulfide detecting
screen at all kinds of angles (even backwards). Rutherford stated that the result was the equal to firing a 15-inch cannon
ball at a piece of tissue paper and having it come back and hit you.
Based on these observations, Rutherford was able to show that the atom had a positively charged nucleus, where all of the
protons were found in a compact group. The positively charged nucleus caused the positively charged alpha particles to be
deflected (bounce off) at a much more severe way than if the protons were randomly distributed throughout the atom. It also
proved that there were large amounts of space between the nuclei, the space taken up by the orbiting electrons. This
experiment is an example of an indirect observation. Even today, no one has seen what a nucleus looks like directly. Only
by indirect means have we been able to come to this current model of the atom.
Purpose: The purpose of this experiment is to simulate Rutherford’s work with alpha particles and gold foil. Our alpha
particles will be marbles. You will simulate his experiment by rolling marbles into a target of marbles and try to determine the
radius of a target marble. The target marbles will represent the nuclei of gold atoms.
Materials:
marbles (11)
book or board
meter sticks (2)
graph paper or computer with graphing capability
pencil
Procedure:
1. In a straight line, place a marble every 10 cm, starting at 0 cm on the meter stick. Behind this line create a box of meter
sticks, with 2 meter sticks up against the wall. The meter sticks and wall will represent the zinc sulfide screen.
10cm
board or book
meter sticks
marble
wall
Diagram not to scale!
You can simulate Rutherford’s work by rolling a marble (the “probe marble”) at a line of marbles (the “target marbles”) and
counting the number of times that there is a collision between the probe marble and a target marble. The target marbles
represent the nuclei of the gold atoms in Rutherford’s gold foil. Count only one collision per roll, not secondary
collisions, if any. We are modeling Rutherford’s alpha particles hitting the gold nuclei so we only want to count collisions
with a nucleus (not anything after it bounces off the nucleus).
2. Within your group, take turns rolling marbles. Roll the marble at the line of marbles 50 times and create a data table to
track the number of hits. Make a sketch of the “screen” and mark a dot where each probe marble (the one you rolled)
hits. If one of your target marbles gets hit, be sure to reset it before your next trial. When observing your marble, consider
questions such as: Do they pass right through? At an angle? Bounce straight back?
Sketch of screen:
Data:
Hits
Misses
Note: Be sure not to intentionally aim your marble at the target (Rutherford’s alpha particles could not be perfectly
aimed at the nuclei of the gold atoms in the foil). To randomize the path of the marble somewhat, roll your marble
down a book or board. Also, do not roll the marbles so fast that they bounce when they hit the floor.
Analysis Questions:
1. Create a histogram based on the class data below. The x-axis of your histogram should be “# of collisions per 50 rolls”
and your y-axis will be “frequency”.
2. You can calculate the radius of the nuclei (target marbles) by looking at the probability of a collision. If you repeat a
large number of rolls at similarly spaced targets, you have measured this probability and can calculate the radius (R)
from the equation below:
hw
R
4tn
where
h is the number of hits
w is the width of the target region (100cm)
t is the number of trials
n is the number of target balls
Note: This formula assumes that the sizes
of the target marble and the probe marble
are the same.
Calculate “R” (radius of the target) for both your data and the class data. SHOW YOUR WORK.
3. How do your calculations for R compare to the actual value of R? Calculate a % error for both your data and the class
data. SHOW YOUR WORK.
4. Which components of the Rutherford experiment did our experiment model?
5. What are some ways that our experiment is not an exact model of the real Rutherford experiment?
6. In this experiment you used indirect evidence to draw conclusions about an object (we are using mathematical
probability to calculate the size of the target and pretending that we can’t see the actual target). Describe some other
instances in everyday life where indirect observation is used to draw conclusions.
7. Describe the pattern of collisions with your screen and the angles at which the collisions occurred. For example, were
the majority at a certain angle? Explain.
8. Based on your sketch of where the probe marble hit the screen, how did this compare to Rutherford’s results (see figure
2.10 in your textbook for a diagram of Rutherford’s apparatus)?
9. The diameter of an atom is approximately 2.2 x 10-10 meters. If the head of a pin is 1mm in diameter, how many atoms
can you line up across the head of a pin? SHOW YOUR WORK.
10. A nucleus of an atom is approximately 1 x 10-14 meters in diameter. How does this compare with the diameter of the
atom given in the previous question? SHOW YOUR WORK.
Fun fact: The gold foil experiment was conducted under the supervision of Rutherford at the University of Manchester in 1909 by
scientist Hans Geiger and undergraduate student Ernest Marsden. Rutherford, chair of the Manchester physics department at the time
of the experiment, is given primary credit for the experiment, as the theories that resulted are primarily his work. Rutherford's gold foil
experiment is also sometimes referred to as the Geiger-Marsden experiment. (from Wikipedia)
References:
This lab was modified from “Rolling with Rutherford” created by Quarknet/Fermilab and the “Rutherford Atom Lab” at http://delagarzascience.wikispaces.com.
Image on page 1 showing schematic diagram of Rutherford’s experiment is from:
http://www.daviddarling.info/encyclopedia/R/Rutherfords_experiment_and_atomic_model.html
© Kristopher Nelson and Mary Sande, Irondale High School, 2012