Experiment – Nuclear Marbles
https://sites.google.com/site/culverphysics/Home/conceptual-physics/lab-nuclear-marbles
Aim:
To determine the diameter of a marble by means of indirect measurement.
Equipment:
• 10 to 15 marbles all of the same size
• 10 to 15 marbles all of a larger size
• 3 x 1 metre rulers
• blu-tac
Theory:
Sometimes it is necessary for people to resort to other methods, besides their sense of sight to determine
the size and shape of things, especially for very small objects, like atoms.
One way of doing this is to fire particles at the object under investigation and study the paths of the
particles that are deflected off the object. Physicists like Ernest Rutherford originally did this by using
radioisotopes. They now use a machine called a particle accelerator, like the Synchrotron at Monash
University. Rutherford indirectly measured the size of the nuclei of gold atoms by studying how alpha
particles were deflected by the nuclei in a sample of very thin gold foil.
In this experiment you will use a simpler, but similar method, to determine the size of a collection of likesize marbles.
You are not allowed to use a ruler (or calipers! or micrometer!) to measure the size of the marbles
directly. Instead you will fire (roll) other marbles at the target "nuclear" marbles and, from the ratio of
collisions to trials, determine their size.
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. This is shown in Figure A.
This is a little bit like throwing stones at a group of similar sized trees whilst blindfolded. If you score
very few hits compared to the number of throws, then you sense that the trees are small.
When you fire (roll) a marble toward a
nuclear marble, you have a certain
probability of a hit occurring between the
rolling marble (RM) and the nuclear marble
(NM).
The probability, P, that a rolling marble will
hit a lone nuclear marble in the target area is
given by
path width
P = target width
The path width is equal to two RM radii plus
the diameter of the NM. This is shown in
Figure B on the next page.
path width
P = target width
=
2R + 2r
L
where
R+r
=
2(R + r)
L
R =
the radius of the NM
r =
the radius of the RM
=
the distance between
the centres of a RM
and a NM that are
touching.
L =
the width of the target
area
If the number of marbles is increased to N, the probability of a hit is increased by a factor of N.
So the probability that the rolling marble will hit one of the N nuclear marbles is:
P =
2N(R + r)
L
The probability of a hit can also be determined by the ratio of the number of hits to the number of trials.
P =
H
T
Where H = the number of hits and T = the number of trials.
You now have two expressions for the probability of a hit. Assume that both of the expressions are
equivalent.
If the radii of the rolling marble and the nuclear marble are equal, then R + r = d, where d is the diameter
of any one of the marbles.
Combine these last two equations for P, and write an expression for d in terms of H, T, N, and L. This is
shown in Figure C.
marble diameter,
d =
This is the formula you are now going to test.
Method & Results:
Step 1:
Place 10 marbles in an area 100 cm wide (L = 100 cm), as shown in Figure A. To stop them rolling away
they can be stuck to the floor using blu-tac. Without looking, roll an additional marble randomly toward
the target area from the release point (about 3 metres away).
If a rolling marble hits two or more nuclear marbles, count it as just one hit. If a rolling marble goes
outside the 100 cm wide area, or if it first hits one of the metre rulers on the sides of the enclosure, do not
count that trial. After each trial remove the rolling marble.
A significant number of trials, more than 200, will be needed before the results will become statistically
significant. Record your total number of hits H and total number of trials T. Now combine your results
with those from the rest of the class.
H =
Hclass =
T =
Tclass =
Step 2:
Use your formula from the Theory section to find the diameter of the marble. Remember to show your
work.
Calculated diameter
d=
cm
Step 3:
Now measure the diameter for five of your marbles using a micrometer and determine an average diameter
for your nuclear marbles.
d1 =
cm
d2 =
cm
d3 =
cm
d4 =
cm
dave =
cm
Average measured diameter
d5 =
cm
Analysis:
1. Compare your result for the computed diameter with your direct measurement of the marble's
diameter. What percentage variation was there between the computed and measured values of the
marble’s diameter?
2. State a conclusion that you can draw from this experiment.
Extension:
Repeat the experiment using nuclear marbles having a larger diameter than the rolling marbles. If there are
not enough larger nuclear marbles make the larger marble your rolling marble.
Those students wanting an A or A+ for this experiment will need to at least make a credible
attempt at this section.
http://wps.prenhall.com/wps/media/objects/439/449969/Media_Portfolio/Chapter_05/FG05_11.JPG
http://www.neoam.cc.ok.us/~rjones/Pages/online1014/chemistry/chapter_8/images/scatter1.gif
Experiment – Nuclear Marbles
Assessment Sheet
Participation
4
3
2
1
0
The student interacted constructively, used their time effectively and used their equipment
appropriately and safely.
The student demonstrated good interaction and use of time and equipment.
The student’s participation was satisfactory and demonstrated some skill in experimental
techniques.
The student’s participation was occasional and required frequent supervision and direction.
The student did not participate constructively or appropriately in the activity.
Understanding
5
4
3
2
1
0
The student demonstrated a comprehensive understanding of the relevant concepts and made
intelligent responses to new information.
The student demonstrated a very good understanding of the relevant concepts with some of the
fine details made clear.
The student demonstrated a good understanding of most of the relevant concepts.
The student demonstrated some understanding of the basic concepts.
The student’s understanding of the basic concepts was rudimentary.
The student did not demonstrate any significant understanding of the relevant concepts.
Analysis
6
5
4
3
2
1
0
The student’s report contained a careful and intelligent analysis of their results to all parts of the
activity, with a clear awareness of sources of error and suggestions for the improvement of
procedures and/or experimental design.
The student’s report contained a very good analysis of their results with a clear awareness of
sources of error and suggestions for the improvement of procedures and/or experimental design.
The student’s report contained a good analysis of their results with a some awareness of sources of
error and suggestions for the improvement of procedures and/or experimental design.
The student’s report contained an adequate analysis of the collected data. However, their written
responses lacked sufficient detail.
The student’s report showed some effective analysis of the collected data but lacked the requisite
detail.
The student’s report showed little effective analysis of the collected data.
The student’s report showed no significant analysis of the experiment.
Reporting
6
5
4
3
2
1
0
Assessment
Grade
Comments:
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams. Their answers to the extension activity were accurate and clearly expressed.
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams. Some of their answers to the extension activity were accurate and clearly expressed.
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams.
The student’s report was clearly written but contained some inadequacies.
The student’s report was fair but contained many inadequacies.
The student’s report was poorly presented and only contained some of the relevant information.
The student’s report lacked significant and relevant substance.
A+
20
A
18-19
B+
17
B
15-16
C+
14
C
12-13
D+
11
D
9-10
E+
8
E
6-7
UG
£5
Experiment - Radioactive Decay and Half-Life
Aim:
To develop an understanding of radioactive decay and half-life.
Equipment:
• per student: 1 polystyrene cup and 20 M&M chocolates, 1 paper napkin
Theory:
Many things grow at a reasonably steady rate. For example: money in the bank, population or the
thickness of a piece of paper that is continually folded over onto itself. Similarly many things decrease at
a steady rate: the value of money in the bank, the amount of vacant land in a place where the population is
growing or the amount of a material that is undergoing radioactive decay.
A useful way to describe this is in terms of half-life, the time it takes for the quantity to be reduced to half
its initial value. For steady decrease, called exponential decrease, the half-life stays the same.
Radioactive materials are characterised by their rates of decay and are rated in terms of their half-lives.
The following experiment will help you to explore this idea.
Method:
Step 1.
Place the M&M's into the cup and cover it with your hand. Shake the cup for five seconds and
then empty it onto your folder.
Remove (and eat!) all the M&M's with the logo side up. These will represent a nucleus that has
decayed. Count these, and record the number in Table A.
Return the others to the cup.
Step 2.
Repeat Step 1 over and over until none of the M&M's remain. Remember to count the number
of M&M's removed each time.
Step 3.
Find the number of M&M's remaining after each shake by subtracting the number removed
from the previous remaining total. Enter your results into Table A.
Results:
Table A
Shake
Number
M&M's
Removed
M&M's
Remaining
Shake
Number
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
10
20
M&M's
Removed
M&M's
Remaining
Class Total Number of M&M's =
Class Results
Shake
Number
M&M's
Removed
M&M's
Remaining
Shake
Number
1
11
2
12
3
13
4
14
5
15
6
16
7
17
8
18
9
19
10
20
Step 4.
M&M's
Removed
M&M's
Remaining
Graph the number of M&M's remaining
against the number of shakes.
Draw a smooth line that best fits the
plotted points.
This graph is to be done on graph paper
and glued into this booklet on the next
page.
Once you have finished plotting your graph and you have answered all of the questions carefully glue
your graph onto this page.
Questions & Discussion:
Question 1
How long did it take for half of the class to 'decay'?
Question 2
How long did it take for half of the remainder (i.e. the next
1
4)
to 'decay'?
Question 3
How long did it take for half of the remainder (i.e. the next
1
8)
to 'decay'?
Question 4
Compare your answers to the last three questions. Is there a pattern? Explain your
answer.
Question 5
What is the meaning of the graph you drew?
Question 6
Approximately what percentage of the remaining M&M's was removed on each shake?
Why?
Question 7
On your graph plot and draw the expected decay curve for the class total of M&M's.
Question 8
Compare your two graphs and discuss any similarities or differences you notice between
them.
Conclusion:
Experiment – Radioactive Decay & Half-Life
Student Self Assessment Sheet
Participation
4
3
2
1
0
The student interacted constructively, used their time effectively and used their equipment
appropriately and safely.
The student demonstrated good interaction and use of time and equipment.
The student’s participation was satisfactory and demonstrated some skill in experimental
techniques.
The student’s participation was occasional and required frequent supervision and direction.
The student did not participate constructively or appropriately in the activity.
Understanding
5
4
3
2
1
0
The student demonstrated a comprehensive understanding of the relevant concepts and made
intelligent responses to new information.
The student demonstrated a very good understanding of the relevant concepts with some of the
fine details made clear.
The student demonstrated a good understanding of most of the relevant concepts.
The student demonstrated some understanding of the basic concepts.
The student’s understanding of the basic concepts was rudimentary.
The student did not demonstrate any significant understanding of the relevant concepts.
Analysis
6
5
4
3
2
1
0
The student’s report contained a careful and intelligent analysis of their results to all parts of the
activity, with a clear awareness of sources of error and suggestions for the improvement of
procedures and/or experimental design.
The student’s report contained a very good analysis of their results with a clear awareness of
sources of error and suggestions for the improvement of procedures and/or experimental design.
The student’s report contained a good analysis of their results with a some awareness of sources of
error and suggestions for the improvement of procedures and/or experimental design.
The student’s report contained an adequate analysis of the collected data. However, their written
responses lacked sufficient detail.
The student’s report showed some effective analysis of the collected data but lacked the requisite
detail.
The student’s report showed little effective analysis of the collected data.
The student’s report showed no significant analysis of the experiment.
Reporting
6
5
4
3
2
1
0
Assessment
Grade
Comments:
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams. Their answers to the extension activity were accurate and clearly expressed.
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams. Some of their answers to the extension activity were accurate and clearly expressed.
The student’s report was very clear and effectively written and made proper use of graphs and
diagrams.
The student’s report was clearly written but contained some inadequacies.
The student’s report was fair but contained many inadequacies.
The student’s report was poorly presented and only contained some of the relevant information.
The student’s report lacked significant and relevant substance.
A+
20
A
18-19
B+
17
B
15-16
C+
14
C
12-13
D+
11
D
9-10
E+
8
E
6-7
UG
£5