Nuclear Physics in Your Browser: Fission, Decay, and Rutherford Scattering

Nuclear physics has a reputation for being abstract — quarks, half-lives, cross-sections, binding energies. But a lot of it becomes concrete very fast once you can run the experiment yourself, even in a browser.

Here's a guide to the nuclear simulations on SciFunLab and what you'll actually learn from them.

Radioactive Decay: The Random Clock

Open the Nuclear Decay simulation and you see 100 atoms on a grid. Each one has a probability of decaying every second based on the isotope you've selected. Click "Start" and watch them blink out one by one — orange glowing as they go.

What makes this useful is the graph panel on the right. It draws two lines simultaneously:

• Orange (actual): the count of remaining atoms, updated each second
• Red dashed (theoretical): N(t) = N₀ × e^(−λt), where λ = ln(2)/half-life

In the first few seconds they match almost perfectly. Then they start to diverge — and that's the point. With 100 atoms, random fluctuations are significant. Increase to 200 atoms and the match tightens. This is radioactive decay, not deterministic formula — the per-atom probability approach shows you why.

The isotopes included:

• Carbon-14 (half-life: 5,730 years, compressed to 1 second in the sim)
• Iodine-131 (8 days)
• Radium-226 (1,600 years)
• Uranium-238 (4.5 billion years)
• Technetium-99m (6 hours — the most-used isotope in medical imaging)

The decay chain panel shows the 14-step sequence from U-238 all the way down to stable Pb-206, with each step labeled as α or β decay and the intermediate isotopes named.

Rutherford Scattering: The Experiment That Killed Plum Pudding

In 1909, Hans Geiger and Ernest Marsden shot alpha particles at gold foil and found that some came back almost the way they came. Ernest Rutherford later said it was "almost as incredible as if you fired 15-inch shells at tissue paper and they came back and hit you."

That result demolished J.J. Thomson's plum pudding model of the atom.

The Rutherford Scattering simulation lets you run this yourself. Alpha particles fly in from the left, and their trajectories curve around a gold nucleus using symplectic integration (which conserves energy properly, unlike naive Euler). The trails are color-coded by deflection angle:

• Blue: less than 1° (most particles — straight through)
• Amber: 1–45°
• Orange: 45–90°
• Red: more than 90° (the "came back" particles that surprised everyone)

At the bottom, side-by-side diagrams compare the Thomson model (uniform positive sphere) vs. the Rutherford model (tiny dense nucleus). Adjust the nuclear charge and watch the scattering distribution shift.

The takeaway is visceral rather than abstract: the vast majority of alpha particles go straight through (empty space), but a tiny number get violently deflected (hitting the nucleus). That pattern is only possible if the mass is concentrated in a tiny point.

Nuclear Fission: Chain Reactions and Control

The Nuclear Fission simulation is the most complex in this set. It models a 700×500 canvas full of U-235 atoms. Fire a neutron and watch what happens.

The physics:

• Slow neutrons (thermal) have ~70% chance to cause fission
• Fast neutrons only ~30%
• Moderator blocks (blue rectangles) slow neutrons down by multiplying their speed by 0.4
• Control rods (gray sliders, 0–100%) absorb neutrons with 90% efficiency

The simulation computes k-effective — the multiplication factor — by comparing how many neutrons exist in the last 60 frames vs. the 60 before that. This updates live:

• k < 1: Subcritical (reaction dies out)
• k ≈ 1: Critical (steady state)
• k > 1.2: Supercritical (red warning, exponential growth)

The "Each fission releases 2–3 new neutrons" insight becomes obvious here: remove the control rods and the reaction explodes in seconds. Add them back and you control it. This is exactly the engineering challenge of a nuclear reactor.

Why These Simulations Work

Text explanations of half-lives, exponential decay, and chain reactions get the formulas across. But there's a level of intuition that only comes from watching 100 atoms decay randomly and noticing they mostly agree with the formula — until there are only 10 left and the randomness dominates.

Or from pulling control rods out too fast in the fission sim and watching the neutron count go supercritical in seconds.

These aren't replacements for the math. They're the complement — the thing that makes the math make sense.

Try them:

• Nuclear Decay Lab
• Rutherford Scattering
• Nuclear Fission Reactor

All free, no account needed.