Analogy Experiment—Projectile Pennies with Rutherford

students shooting pennies at the whiteboard

Atomic theory is a common topic throughout any introductory chemistry course. Regardless of the depth given to the various models and the evidence that led to their creation, it’s likely that Rutherford’s gold foil experiment gets at least some attention in your course.

Editor’s Note: The activity described here has been revised and updated. Some of the changes have been made with the help of comments from readers. If you are logged into your ChemEd X account, you can see those comments at the conclusion of this post. You will find the updated activity HERE.

For me, this topic had always been a bit more lecture-based. Even though I thoroughly enjoyed talking about the history and development of the atom, I didn’t like the feeling of being heavily reliant upon lecture. Additionally, I didn’t like the fact that I wasn’t providing students with an opportunity to generate their own evidence to support the concepts and models that I wanted them to develop. In this post, I propose a simple activity that gives students an opportunity to replicate Rutherford’s experiment through an analogy experiment that may allow for easier conceptualization of the experiment itself and provide additional support for model development.

Before I mention anything to my students about Rutherford’s experiment, I introduce them to an analogy experiment called Projectile Pennies. Though students don’t yet know what exactly this is an analogy to, they will shortly. It is not imperative that they understand the analogy yet anyway. The goal of the experiment is presented to them as follows:

Indirectly calculate the diameter of an unknown object by recording the number of times it is hit with objects of a known diameter.

The key idea here is to emphasize the fact that they will be determining the diameter of something indirectly. All students understand what they would do if I asked them to determine the diameter of a circular object placed in front of them—simply measure it. But what if they were not able to see the object? Obviously this complicates things a bit. This provides a nice opportunity to discuss how often (especially in chemistry) we rely on indirect evidence to help us inferences about the primary claim that is being made.

The experimental setup (figure 1) and the materials needed are simple. Each group receives two meter sticks, 20 pennies, a whiteboard, and an object with a circular bottom. Typically, I give the groups full water bottles to ensure they have enough mass, but you can use different items with a variety of sizes (film canisters, water filled beakers...). 

Figure 1: Side view of experimental setup (left). Top view of experimental setup (right).


One person in the group is designated as the “penny shooter.” While the other members of the group are getting set up, the penny shooter is told to wait out in the hall to avoid knowing the location of the unknown object. Ideally, we want the penny shooter to be unaware of the location of the object to limit the possibility of intentionally shooting pennies directly at the object. In this past, I have tried to decrease this bias even more by blindfolding the penny shooters and allowing them to wear headphones with music playing on full volume. Needless to say, students fight over who gets to be the penny shooter.

The other member(s) of the group have a few simple tasks before and during the experiment.

Getting Set Up

As seen in figure 1 above, students will establish the path by laying down two parallel meter sticks between 70 – 90 cm apart. Place the whiteboard on top of the meter sticks so it is just barely above the ground and can easily lean against a wall, desk, or lab table. Though the figure above suggests leaning it against a wall, it is easier for the group if the whiteboard can lean against something that does not allow pennies to come back unless they hit the unknown object. Once the whiteboard is secure, place the object somewhere behind the whiteboard. Do not place the object directly next to the meter sticks. Before they tell the penny shooter to come in, ensure that a penny can slide under the whiteboard and that the object cannot be seen from the shooter’s perspective.

During the Experiment

The penny shooter will essentially slide the penny toward the whiteboard (the penny should not leave the floor at any point). Once the penny shooter is ready to begin firing pennies, the other group members have a few simple tasks:

  1. Record the number of times the object is hit.
  2. Ensure a clear path for the pennies (i.e. if a penny hits and then comes back, remove it from the path).
  3. Once a round is over, collect the pennies and hand them back to the penny shooter for the next round.

Figure 2: Experimental Setup—Photo taken in my classroom


Typically, I tell each group that they need to fire at least 100 pennies (5 rounds of 20). If we have enough time, I may ask for more but 100 is usually sufficient. Once they have reached the appropriate amount of pennies fired, they record their data and any measurements made in the following table:


Table 1: Organizing data from the experiment


Once they have all the necessary data, I provide them with the equation below, which will allow them to calculate the experimental diameter of their unknown object.

Figure 3: Equation used to calculate experimental diameter of unknown object


Personally, I decide to give them the equation above simply to save time. However, I can imagine some teachers possibly adding a layer of depth to the investigation by having students derive the equation themselves. Once students have calculated the experimental diameter of the unknown object, they are asked to compare it to the known diameter. Though results will vary, several groups often get within 1 – 1.5 cm of the known diameter—pretty cool! From this experience, students gain insight as to how it is possible to determine the size of an object that cannot be seen.

Figure 4: Example data and calculation of diameter


Lastly, I provide four extension questions for each group to answer. Each question is meant to get students thinking about some of the inferences that will soon be made once we start talking about Rutherford’s experiment.

  1. If you were the one firing the pennies while doing the same experiment and you noticed that some of your pennies actually bounced back toward you, how would you interpret this observation?
  2. What would this suggest about the mass of the unknown object relative to the penny?
  3. If you knew that your penny had a positive charge and you witnessed the same effect, what could you conclude about the charge of the unknown object?
  4. Why did the majority of your pennies not hit the unknown object?

Once we eventually get to discussing Rutherford’s experiment, it is fun to see students make the connections between his experiment and our analogy. I will often hear things like, “Oh, so the alpha particles were just like our pennies!” and other statements describing the similarities between the nucleus and unknown object. Even the realization as to why the majority of pennies did not make contact with the unknown object being similar to the majority of alpha particles going straight through the gold foil is a cool one to hear. I believe having this experience prior to discussing Rutherford’s experiment provides a strong foundation for our students to more easily connect the rather conceptual findings from Rutherford’s experiment. I feel it is better than simply discussing the details of Rutherford’s experiment head on and assuming everyone will just “get it.” When teaching such abstract concepts in chemistry, the more connections we can allow our students to make with previous experience, the easier they will be able to assimilate such experiences with the appropriate concept.


atomic theory, Rutherford, golf foil experiment, alpha particles, nucleus, electrons

Procedure time: 
30 minutes
Prep time: 
10 minutes
Time required: 

About 30 minutes before the discussion.


two meter sticks, 20 pennies, a whiteboard, and an object with a circular bottom (water bottle, soup can, etc).


Have students complete the procedure below and answer the questions before discussing the theory that Rutherford came up with based upon the results of his gold foil experiment.


When logged on to your ChemEd X account you will find the procedure in the Student Document included in the Supporting Information below.

  1. If you were the one firing the pennies while doing the same experiment and you noticed that some of your pennies actually bounced back toward you, how would you interpret this observation?
  2. What would this suggest about the mass of the unknown object relative to the penny?
  3. If you knew that your penny had a positive charge and you witnessed the same effect, what could you conclude about the charge of the unknown object?
  4. Why did the majority of your pennies not hit the unknown object?




Gather the materials and provide the goal of the experiment to students.


I do not remember where I heard about this activity initially, but I have been using some form of it since very early in my career. I have seen a variety of versions online. 

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Comments 12

Dane Travis | Sun, 11/03/2019 - 11:34

I did this activity with 2 classes and the outcome was quite poor. Only 1 in 12 groups got data that was near the expected value.  When the results were so bad for my first class, I thought it was because once the penny slider knew approximately where the object was he/she just kept sliding them to the same place.  For that reason I had the object moved after each 20 penny trial and found the data to be just slightly improved. The only option I can think of is to try is to have the object moved after *each* penny is sent through.  (I did check the students' math work and it was correct.)

Any other ideas?

Ben Meacham's picture
Ben Meacham | Sun, 11/03/2019 - 13:30

If you still have access to any of their original numbers, see what happens to the results when you subtract the actual radius of the penny instead of subtracting (2 x Diameter) -- see equation below. This was the equation I used to use and it's also the one taken directly from the Modeling Instruction curriculum but I switched it up last year so it's totally possible that my reasoning for changing the equation was wrong.  Please let me know what you find!  Hope that helps.

Dane Travis | Sun, 11/03/2019 - 16:26

I don't think that was the problem because all of their numbers were too high, not too low.

Ben Meacham's picture
Ben Meacham | Mon, 11/04/2019 - 12:26

What is the total number of pennies they shot?  In your original comment, you had mentioned the phrase "20 penny trial" and I'm just wondering if that meant they only shot 20 pennies total or something else.  

Dane Travis | Tue, 11/05/2019 - 07:04

They shot 5 sets of 20 pennies each.

I used soup cans as the object.


John Yohe | Sat, 11/09/2019 - 21:04

If the pennies are not shot somewhat evenly over the whole area and are focused too closely around the target you will get a larger diameter. Maybe consider making sure placement is random and having the can move locations between sets to help with the randomness. My guess is there will be some bias to target the center subconsciously.

Dane Travis | Mon, 10/25/2021 - 13:37

I've worked with the physics teachers on this and we can't figure out the -2d.  To us the equation should be:

D = H * (W-2r)/T

r is the radius of the penny.

Please, someone either explain the "-2d" or agree with our equation above!


Ben Meacham's picture
Ben Meacham | Tue, 10/26/2021 - 15:56


After looking at your proposed equation, I replicated the analogy experiment again and got a calculated diameter that was within 3% of the actual diameter of the "unknown object"! In other words...I definitely agree with the new equation. After giving it a bit of thought, it made a lot more sense. I plan to update the blog post to include this new equation. Thank you for finding a more accurate way to calculate this so it can provide a better experience for both students and teachers!  

Chris Leverington | Thu, 11/14/2019 - 10:35

I would think that once they hit the object one time...they would tend to shoot it in the same vicinity after that because they know where it is.

Ben Meacham's picture
Ben Meacham | Thu, 11/14/2019 - 12:43

Not sure if I mentioned this in the original post but this is why I tend to tell the shooters to wear a blindfold and headphones w/ music on.  Blindfolds are easy since it could just be some item of clothing and these days at least one of the students will have headphones to use.  This has been the best way I've found to improve the randomness in their shooting.

Renee Haugen | Sun, 11/17/2019 - 16:03

Yes, I experienced this as well. I noticed immediately that once they hit the cup, they aimed for the cup, giving a disproportionate number of hits, resulting in a higher diameter. Even when I warned the next class to find a way to make it random, they had a hard time--it seems human nature to aim for the cup once you hit it!   

One thing I noted students doing that led to a better result was putting 10 pennies down at a time and sliding them all with one hand. Then they could not be aimed at the cup!   

Another solution was to line the pennies up in a row across the front of the board from left to right and then quickly slide one after the other without stopping. That way the entire space was covered and the pennies hitting the cup were proportionate to the space it occupied, which of course was really the goal.   

I really like the mathematical relationship here. In an honors class I would have had them propose the mathematical relationship themselves. As it was instead I gave them the formula and ask them what it was doing. They quickly figured out that it was simply the percentage of times the pennies hit the cup x the total distance under the board. When I asked them about the subtraction of 2x the diameter of the penny, I quickly had students who were able to propose an answer. I was very impressed with both their ability and willingness to figure this out as well as the beauty of the activity that allowed it. It allowed us to brainstorm ideas that might make it work!

Deanna Cullen's picture
Deanna Cullen | Mon, 11/08/2021 - 16:06

Thanks to the help of readers, Ben has revised and updated this activity. Please see the updated post. I am closing the comments on this version. The new version is open for comments. Thank you!

Deanna Cullen

ChemEd X High School Editor