Nuclear Marbles
Determining the diameter of a marble by indirect measurement
Materials:
9 marbles
3 meter sticks
Some times scientists are called upon to calculate the measurement of something that can
not be directly measured such as the diameter of the nucleus of an atom.
Problem: You need to indirectly measure the diameter of a marble. You are not
allowed to directly measure the marble. Instead, you will roll other marbles at the target
“nuclear” marbles and, from the ratio of collisions to trials, determine their size. This is a
little bit like throwing snowballs at a car while blindfolded. If you score very few hits
you sense that the car is small. If you hit it a lot then you sense the car is large.
First, use a bit of reasoning to arrive at a formula for the diameter of the nuclear marbles
(NM). Then at the end of the experiment you can measure the marbles directly and
compare your results.
When you roll a marble toward a nuclear marble,
you have a certain probability of a hit between the
rolling marble (RM) and the nuclear marble
(NM). One expression of the probability P of a
hit is the ratio of the path width required for a hit
to the width (l) of the target area Se Fig A. The
path width is equal to two RM radii plus the
diameter of the NM, as shown in Fig B. The
probability P that a rolling marble will hit a lone
nuclear marble in the target area is:
P = (path width)/(target width) = (2R + 2r)/L
If the number of nuclear marbles is increased to
N, the probability is increased to:
P = 2N (R + r)/L
The probability of a hit can also be determined experimentally by the ratio of the number
of hits to the number of trials.
P = H/T
If (R + r) is equal to d (diameter) then solve for the diameter of the marble in terms of
H,T,N, and L.
Marble diameter d = __________________
Let’s put your formula to the test.
Procedures:
1. Place 8 marbles in an area 60 cm wide as in fig A. Roll another marble into the
area blindly and record all hits and all trials. Throw at least 200 trials.
a. A hit is any hit on the way into the area prior to striking the back of the
target. (You can only get 1 hit per throw.) Multiple hits do not count.
b. A miss is when the marble passes all the way through the area with out
striking the back.
c. Each time a marble is thrown it is counted as a trial.
2. Record all Hits and Trials.
a. Hits = __________
b. Trials = _________
3. Use your formula and calculate the diameter of the marble.
4. Using a Vernier caliper measure to diameter to the most accurate level.
5. Calculate your percent error.
Questions:
1. After completing this experiment what was your reaction to the accuracy of the
activity and what conclusion could you draw from this activity?
2. How could this technique be used in laboratories around the world?
3. Describe how Ernest Rutherford could have used this lab with the gold foil
experiment.