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Indirectly Measuring the Atom Mark as Favorite (14 Favorites)

LESSON PLAN in Inferences, History, Model of the Atom, Atomic Theory, Atomic Radius. Last updated March 15, 2021.


In this lesson, students will try to determine the radius of one circle and the total area of multiple circles on a piece of paper by indirect measurement. They will relate this to the experiment done by Ernest Rutherford in which he bombarded a gold foil with Alpha particles.

Grade Level

Middle School and High School

NGSS Alignment

This lesson will help prepare your students to meet the performance expectations in the following standards:

  • MS-PS1-1: Develop models to describe atomic composition of simple molecules and extended structures. 
  • Scientific and Engineering Practices:
    • Using Mathematics and Computational Thinking
    • Developing and Using Models
    • Analyzing and Interpreting Data


By the end of this lesson, students should be able to:

  • Use indirect evidence to determine the space occupied by “atomic nuclei” (circles) representing the atom on a piece of paper.
  • Explain how this method of measurement is similar to the way Ernest Rutherford determined that the atom is mostly empty space and how much area was taken up by an atomic nuclei.
  • Compare and contrast this experience to the Gold Foil experiment.

Chemistry Topics

This lesson supports students’ understanding of

  • Atomic Structure
  • Atomic Radius
  • Atomic Theory
  • Model of the Atom


Teacher Preparation: 20 minutes
Lesson: 80 minutes

  • Warm-up: 20 minutes
  • Hands-on activity: 50 minutes
  • Class discussion: 10 minutes

Materials (per group)

  • One ½ inch ball bearing (can substitute a marble)
  • Nuclei Template Sheet
  • One sheet of carbon paper
  • Tape
  • Metric ruler


  • No specific safety precautions need to be observed for this activity.

Teacher Notes

  • I suggest that students work as partners for this lesson.
  • The hands-on portion of this activity was modified from a Cambridge Physics Outlet (CPO) activity, found in the Foundations of Physical Science lab workbook (2006).
  • This lesson should be used after students have learned about Democritus’ atom theory, and the progression to J.J. Thompson’s Plum Pudding Model.

Warm-up activity:

  • Students should watch the AACT Ernest Rutherford video (~5 minutes) and complete the accompanying video questions. The questions may be completed as a class and/or reviewed together prior to moving on to the activity portion of the lesson.
  • Teachers may choose to show an additional video describing Rutherford’s Gold Foil Experiment from Backstage Science. This video details the same experimental design with updated detector technology.
  • The warm-up activity should begin a discussion about our current understanding of atomic structure and Rutherford’s contribution.

Hands-on Activity:

  • In my experience, many students have never used carbon paper. Teachers may need to model the setup:
    • Place the carbon paper shiny side up.
    • Place the nuclei template face down on top of it, so that the entire surface of the nuclei template is touching the carbon paper.
    • Tape the papers to the tabletop.
  • Carbon paper can be purchased at office supply stores or Amazon. Alternatively, coloring on a piece of paper with a black crayon will produce similar results.
  • Depending on your room setup, you can complete the experiment on a desktop or on the floor if you have a tile floor.
  • The teacher may want to change the size of the circles template for different groups and examine if size of nuclei will affect results as an extension.
  • The circles template was made to resemble the gold foil with an outer circle as the electron cloud and the inner circle as the nucleus. After the activity, explain that this template (model) of “atoms” is not to scale.
  • An answer key has been provided for teacher reference.


  • A short extension worksheet that includes several data-driven practice questions has been included as an option for teachers to use. An accompanying answer key document has also been provided for teacher reference.

For the Student



In the early 20th Century Ernest Rutherford, a physicist from New Zealand, was trying to better understand the structure of the atom. His predecessor J.J. Thompson proposed the Plum Pudding Model of the atom in which negatively charged particles were embedded in a positively charged matrix. Rutherford and colleagues Hans Geiger (which the Geiger counter was named after) and Ernest Marsden setup an experiment to determine more completely the structure of the atom.

Prelab Question

  1. Describe how you can determine the mass of a single card in a deck of cards (placing one card on a scale will not register a mass reading).


To determine the area of “atomic nuclei” circles on a piece of paper using indirect measurement. Then, connecting the process to Rutherford’s Gold Foil Experiment.


  • Tape   
  • Carbon paper
  • Nuclei template sheet
  • ½ inch ball bearing or marble   
  • Metric ruler


  1. Place a single piece of carbon paper face up (shiny side) on your desk.
  2. Place the Nuclei template sheet face down over the carbon paper and tape it to the surface of the table. The entire template sheet should be in contact with the carbon paper.
  3. Drop the ball bearing 75 times on the paper.
  4. Attempt to randomly scatter the drops throughout the entire surface of the paper (don’t drop from the same spot every time).
  5. Your partner will now drop the ball bearing 75 times on the same paper, so that the total drops for your group equal 150. 
  6. Your partner should also attempt to randomly scatter the drops throughout the entire surface of the paper (don’t drop from the same spot every time).
  7. When 150 drops have been completed, remove the tape and return the carbon paper to your teacher.


See directions written below the data table for guidance for completion.

1. Number of marks on paper
2. Number of marks completely inside inner circles
3. Area of paper (cm2)
4. Total area of circles (cm2)
5. Estimated area of 1 circle (cm2)
6. Radius of a circle (cm)
7. Calculated area of 1 single circle (cm2)
8. Percent error (%)

Data Table Instructions

  1. Number of marks on paper: Count the total marks (resulting from drops) on your Nuclei template sheet paper and record in the data table above. (Note: It is ok if you have more than 150 marks, count them all.)
  2. Number of marks completely inside inner circles: Count the total number of marks that fall completely inside a small inner circle on the template sheet. Do not count the marks that fall within the larger outer circles. Record your answer in the table above.
  3. Area of the paper: Use the metric ruler to measure the length and width of the paper in centimeters to the hundredths place. Show your work below, then record your answer in the table above.
  4. Total area of circles: Set up a ratio to find the total area of the circles on the paper. Use the equation:

    Calculate the amount of total area of the small circles, this is your unknown or “X”
    Show your work, and then record your answer in the table above:
  5. Estimated area of 1 circle: Complete this task by taking your calculation for the total area of the circles and dividing that by how many small circles are on the paper. Show your work, and then record your answer in the table above:
  6. Radius of a circle: Now let’s see how accurate your estimate for the area of a circle is. Using your metric ruler, measure the diameter of a single circle in centimeters and divide by two to get the radius. Record it in the data table above.
  7. Calculate the area of 1 single circle: Use the equation:  . Show your work, and then record your answer in the table above:
  8. Percent Error: Calculate your percent error by using the equation:

    For this activity:

    Show your work, and then record your answer in the table above:

Analysis Questions

  1. In this activity, what did the nuclei template paper, the carbon paper and the ball bearing each represent? How is our activity similar to Rutherford’s original experiment? In what ways does it differ?
  2. What was an important conclusion of Rutherford’s experiment and how did he come to this conclusion?
  3. What are some possible causes of error in this activity?
  4. Obtain the percent error for each group in class. Calculate an average percent error for the class below (show work). How does the addition of multiple lab groups data effect the overall percent error and why?
  5. Could Rutherford have determined his percent error as you have in this experiment? What is the major difference? What else could he have done to confirm his results?
  6. Explain the meaning of indirect evidence and how this experience relates to Rutherford’s experiment.