Rutherford’s experiment
A marble simulation lab
Name ____________________
Background:
In 1911, a series of experiments carried out under the direction of Ernest
Rutherford that shaped our ideas about the nature of the atom and disproved J.J.
Thomson’s model of the atom. (Thomson believed that the atom consisted of a positively
charged jelly-like mass with negatively charged electrons within it.) The experiments
were conducted by James Geiger, a German physicist working with Rutherford, and
Ernest Marsden, an undergraduate at Cambridge. They bombarded a thin piece of gold
foil with α-particles (helium nuclei). With a fluorescent screen, they observed that most
went through the foil without changing directions. A few were reflected back at acute
angles. The relative number of alpha particles reflected at different angles was counted.
By mathematical analysis, Rutherford was able to show that the scattering pattern was
caused by a small, positively charged center within the gold atom. Rutherford was able
to show that this central nucleus contains more than 99.9% of the total mass of the atom
and has a diameter of only 0.01% of the atom itself! (The calculated density of the
nucleus is about 1 x 106 tons/cm3!)
In this lab you will conduct an experiment similar to Rutherford’s to determine
the diameter of a marble. Two marbles will serve as “small, positively charged nuclei”
and the other two marbles will represent α-particles.
Purpose: To determine the diameter of a marble using a technique similar to the one
used in Rutherford’s gold foil experiment.
Materials: 4 marbles, ruler, several books or notebooks, masking tape
Procedure:
1. On a flat surface (either the floor or lab table) put 2 books approximately 40 – 50 cm
apart. Measure the width of the target area (distance between the books) in mm and
record.
2. Put 2 glass marbles between the books. Place a piece of masking tape under the
marbles.
3. Place a visual barrier about 1 meter from the books. (A binder standing upright works
well).
4. Assign each partner a job: “α-particle Generator” and “Recorder”. (You will switch
jobs half way through the lab.)
5. The “α-particle Generator” will stand behind the visual barrier and roll the 2 remaining
marbles towards the stationary marbles. Roll the marbles one at a time.
6. The “Recorder” will catch the marbles after they roll through the books and record on
the data table if the roll was a hit or miss. A hit is recorded only if the α-particle hits
the stationary marble without interference. (If it ricochets off the wall, it is a miss.)
7. After 100 rolls, the partners should switch jobs.
8. A minimum of 200 rolls must be completed. (You may do more than 200 if time
permits.)
1
book
w
a
l
l
marbles
visual barrier
(~ 1 m from books)
book
Mathematical Theory:
The probability of hitting the stationary marbles depends upon the diameter of the
marbles, the width of the target area, and the number of stationary marbles.
•
•
•
The probability of hitting a marble is directly proportional to twice the diameter
of the marble (2D).
The probability of hitting a marble is inversely proportional to the width of the
target area (W).
The probability of hitting a marble is directly proportional to the number of
target marbles (N).
This information can be used to create the following equation for the probability of
hitting a marble:
Probability = 2(D) * N
W
The probability is also defined as:
Probability = H
T
where H = number of hits
T = number of throws
By setting the two equations equal to each other, the new equation becomes:
Equation A
H = (2D)*N
T
W
Data Table:
Width of target area (W)
mm
Number of hits (H)
Number of throws (T)
2
Rutherford’s Experiment Lab
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Hit
Miss
#
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
Hit
Data Table
Miss
#
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
Hit
Miss
#
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
Hit
Miss
#
Hit
Miss
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
3
197
198
199
200
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
Questions:
1. Solve for the diameter (D) of the marble using equation A and your values for H, T, N,
and W. Show your work.
2. Assuming that the actual value for the diameter of the marble is 15 mm, what is the
percent error of your measurement?
3. Describe one way that you could get a more accurate measurement for the diameter of
the marble.
Conclusion: In your conclusion indicate how the activity relates to Rutherford’s gold
foil experiment. Also include all sources of error that may have affected your results and
any ways in which the experiment could be improved.
4