Investigating Science 11–12 · Year 11
Finding a hidden target with rolling marbles: a model of Rutherford scattering
Module 3: Scientific Models
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
Like Rutherford’s team, the learner infers the size and shape of something unseen from how often and how projectiles are deflected, and the inference sharpens as the number of trials grows.
What you need
- a board 50 cm wide raised 2 cm above the bench on spacers, with a hidden cardboard target of unknown shape (5 to 15 cm across) fixed underneath
- 16 mm marbles, a launch ramp, a strip of paper along the exit side to mark where marbles leave
- a random number table or app to choose launch positions across the 50 cm width
How to do it
- Roll a marble from a randomly chosen position straight under the board; record whether it was deflected and where it came out.
- Make 100 rolls and calculate the fraction f that were deflected.
- Estimate the target width w = fW − d, where W = 50 cm and d = 1.6 cm.
- Use the directions of the deflected marbles to sketch the target’s shape.
- Repeat with 25 rolls and 400 rolls (pooling groups) and compare the spread of estimates.
- Lift the board, measure the target and compare with PhET’s Rutherford scattering model.
What you should see
For a 10.0 cm target, 1.6 cm marbles and a 50.0 cm launch width, the chance of a hit is (10.0 + 1.6)/50.0 = 0.232, so about 23 of 100 rolls are deflected with a standard deviation of 4.2 rolls. From 100 rolls the width estimate is 10.0 ± 2.1 cm (one standard deviation); pooling 400 rolls halves the uncertainty to ± 1.1 cm. A round target sends marbles out at a spread of angles; a flat face sends them back along a single direction.
What changes
- What you change
- number of rolls (and target shape)
- What you measure
- fraction deflected and inferred width
- What you keep the same
- same launch speed from the ramp
- random launch positions
- same marbles
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Scientists saw the nucleus directly.
- A few trials are enough to know a hidden shape.
- Most of an atom is solid matter.
Safety card
Hazards
- marbles on the floor are a slip hazard
Controls
- catch tray at the exit side
- count marbles in and out
Note
No hazardous chemicals or heat sources: record the activity in the school's RiskAssess risk assessment, following the NSW Department of Education Science safety and compliance page; the Chemical Safety in Schools package is not triggered.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Investigating Science Stage 6 Syllabus (2017), NESA; currentINS11-10INS11/12-2INS11/12-3INS11/12-4
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.