Source
Each source is a real radioactive substance that shoots out alpha particles with a fixed energy, measured in MeV. You don't need the definition — just know: more MeV means a faster, harder-to-turn alpha. For one particle, a few MeV is an enormous kick; on a human scale it is unimaginably tiny. Radium C′ is the source Rutherford's team used most.
Alphas to fire
Time
Aim
centreedge (1r)

The Test Bench is not the historical experiment — in reality nobody could aim. It is here so you can study how closeness, energy, force, and deflection relate.

Coulomb and the Atom — Introduction

Reset the experiment?

The stage will clear either way. What should happen to the rows already in your data table?

Switch data table?

Summary rows and slow-motion measurements use different data tables. Switching replaces the current table and its rows.

Coulomb and the Atom

Fire alpha particles at a gold foil — one at a time, as it really happened — and read the flashes on a detector ring. The rare violent deflections, combined with Coulomb's law, let you work out for yourself how the atom's positive charge is arranged.

How do I explore?

A radioactive source fires alpha particles — tiny, fast projectiles carrying a positive charge of +2e — at a gold foil. Gold's atomic number is 79, so each gold atom holds a positive charge of +79e somewhere inside it. Where that charge sits is not shown. That is the question this experiment answers.

There are two places to work:

  1. The Experiment — as it really ran. Alphas arrive one at a time, by chance, and their paths are invisible: all you see is a flash on the detector ring where each one lands. Real time shows flashes at the true counting rate (the original team watched like this for months). Accelerated finishes a run of thousands in seconds. Press Play to start.
  2. Test Bench — here, and only here, you may aim. Send single alphas closer and closer to one magnified atom's centre and watch what changes. Slow motion replays a shot with a live force readout. The Bench is not the historical experiment — it exists so you can study the relationships.

What should I do/notice?

  • In the Experiment: where do almost all the flashes land? How long do you have to watch before anything else happens? The Rarity column turns that wait into a number.
  • On the Bench: aim closer and closer to the centre. Where does anything start to change? The rare hard turns take a Max force of tens of newtons — roughly the weight of a textbook, acting on one sub-atomic particle.
  • Coulomb's law connects force, charge, and distance. How close to gold's +79e must an alpha come to feel a force that big?
  • An atom is about 10−10 m across. Compare that to the distance you calculate.

What about the data?

The Experiment counts flashes, exactly as the real one did — so its table holds counting results: four rows per batch, one for each deflection band (None <1°, Some 1–5°, Large 5–90°, Backscattered >90°), with the Count and the Rarity (1 in N) in that band. Plot Count or Rarity against Deflection to see the whole distribution; run batches at different energies and compare. A blank Rarity means that band saw nothing — which can itself be the finding.

Test Bench shots get one row each — Max force (N), Closest approach (10−14 m), Deflection angle (°), Outcome, Min KE (% of launch), Source, Energy (MeV).

Slow motion (Bench) replaces the table with one alpha's measurements over time — Alpha #, Source, Time (10−18 s), Force (N), Speed (million m/s), Deflection (°), KE (% of launch). Fire several and compare them by Alpha #.

Accessibility

  • Tab / Shift+Tab move through the control panel; arrow keys change the selected option; the toolbar has Play/Pause, Reset, and Info.
  • All controls work with touch. Flash landings, run results, and rare events are announced to screen readers.

Fire alpha particles at a gold foil — one at a time, as it really happened — and read the flashes on a detector ring. The rare violent deflections, combined with Coulomb's law, let students work out for themselves how the atom's positive charge is arranged.

Standards

HS-PS2-4 Students invert Coulomb's law — real constants, real newtons — to bound how close the rare alphas came to the atom's positive charge.
HS-PS3-5 The slow-motion flyby shows the force peak and the KE trough happening together: kinetic energy converts to electric potential energy and back.

Design intent

The Geiger–Marsden (Rutherford) gold-foil experiment, rebuilt so students derive the conclusion instead of hearing it. Nothing about the atom's interior is drawn, named, or exported — the intro slides frame the mystery but deliberately withhold what was found. Two lines of reasoning are in the data:

  • Magnitude: a ~20 N Bench shot inverts to r ≈ 4×10−14 m — thousands of times smaller than the atom. An upper bound; higher-energy sources probe deeper and tighten it.
  • Rarity: the Experiment is honest — ~1 backscatter in 8,000, no seeding. A 1,000-alpha batch may show zero; that is the finding.

The two spaces divide the labor: The Experiment is the historical truth (one alpha at a time, invisible flights, counting by angle — real time makes the months tangible) and exports only what counting could measure. The Test Bench is openly hypothetical (aiming that reality never allowed) and carries the mechanism: force, closest approach, energy. The stage labels which is which.

The step that closes the argument (hold until students hit it)

Inverting the point-charge formula assumes the +79e acts from one place. If it were spread across the whole atom, the largest force it could exert anywhere is ~2×10−6 N; the measured spikes exceed that by a factor of ten million, so the charge cannot be spread out. Offer as a challenge question, not a given.

Worked inversion (for reference)

k·q₁·q₂ = (8.99×10⁹)(2×1.6×10−19)(79×1.6×10−19) ≈ 3.65×10−26 N·m². For F = 21 N: r = √(3.65×10−26/21) ≈ 4.2×10−14 m — over two thousand times smaller than the ~10−10 m atom.

Historical grounding: the three sources are real members of radium's decay chain, and Radium C′ was Geiger and Marsden's main source (they varied energy with mica sheets); the ~2 flashes/s counting rate is representative of the dark-room scintillation work. The reveal — that the tiny region is called the nucleus — belongs in your closer, after the inference. The word never appears in the sim.

Discussion prompts

  • After a few minutes of real time: how would it feel to do this for months? Why keep going?
  • In slow motion: when exactly did the force peak — and what was the kinetic energy doing at that moment?
  • Could +79e spread evenly through the whole atom bounce an alpha back?
  • Compare batches across sources: why does the higher-energy beam deflect less often, yet probe closer on the Bench?

Data format

Three tables; switching prompts first, then replaces. Experiment: four rows per batch — Batch #, Source, Energy (MeV), Alphas fired, Deflection band, Count, Rarity (1 in N; blank = that band saw nothing). Partial runs export partial batches. Bench shots: one row each — Max force (N), Closest approach (10−14 m), Deflection angle (°), Outcome, Min KE (%), Source, Energy. Slow motion: time series — Alpha #, Source, Time (10−18 s), Force, Speed, Deflection, KE.

Good plots: Count or Rarity vs. Deflection band (filter out "None" to see the tail); Rarity vs. Energy filtered to Backscattered; Max force vs. Closest approach (inverse-square in plain sight); Force and KE vs. Time by Alpha #.

Honest numbers: everything follows the exact Coulomb-scattering relations with real constants; the Bench aim scale is log-mapped in fractions of r, while exported distances stay in metres — the compare-to-the-atom step is the student's move.