Less than a gram: a nuclear weapons physics simulator for NCEA Physics
There's one number in this whole topic that stops a class dead. The bomb that destroyed Hiroshima released its energy by converting less than a gram of matter. Not a gram of uranium — a gram of mass, vanished, turned entirely into energy. Everything else in the physics of nuclear weapons is an unpacking of that single sentence, and this simulator is built to make it land.
A word on scope first, because the subject demands it. This tool covers the physics that AS91172 assesses: how much energy comes from how little mass, why a chain reaction can run away, and why a reactor can't. It deals in mechanism and principle only. There is nothing here about how a device is engineered — no critical-mass figures as design targets, no assembly mechanisms, no specifications. Those aren't in the standard and aren't in the tool. What is here is some of the most striking physics in the whole course.
It's a single self-contained web page — open it in a browser, put it on the projector, done. Below I'll walk through the physics across its four screens, then flag some ways to use it.
E = mc², made concrete
Students meet E = mc² as a famous equation long before they meet it as a calculation. The first screen turns it into arithmetic they can follow.
Pick a device — Little Boy, Trinity, Fat Man, or one of two much larger test devices — and the screen shows the energy released and the mass that had to disappear to produce it. For Hiroshima's roughly 15 kilotonnes (6.28 × 10¹³ joules), you rearrange the equation to find the mass:
Δm = E / c² = 6.28 × 10¹³ / (3.00 × 10⁸)² ≈ 7 × 10⁻⁴ kg
Less than a gram. The animation shows that speck of matter on one side and the energy pouring out on the other, and the contrast is the entire point. A city was destroyed by converting a fraction of a gram of matter completely into energy.
There's a second number here that's easy to conflate with the first, and the tool keeps them apart deliberately. About 0.7 grams of mass disappeared, but about 0.76 kilograms of uranium fissioned. Those aren't the same thing. The uranium nuclei that split are still there afterwards — they've become lighter fragments, and it's the tiny difference in mass between the original nucleus and its fragments, multiplied by c², that comes out as energy. Students who grasp that distinction understand mass defect properly; students who don't tend to think the whole kilogram of uranium turned into energy, which is off by a factor of a thousand.
The chain reaction, and the tyranny of exponential growth
One fission releases energy and a couple of spare neutrons. If those neutrons go on to cause further fissions, and those release more neutrons, you have a chain reaction. The second screen lets you control it with a single number: k, the number of neutrons from each fission that go on to cause another.
Set k below 1 and the reaction dies out — each generation is smaller than the last. Set it to exactly 1 and it holds steady, which is a reactor at constant power. Set it above 1 and the numbers double, and double again, and again. This is the difference between a power station and a weapon, and it's a single slider.
But the real lesson of this screen is what exponential growth actually feels like, and it's genuinely counterintuitive. Run the chain reaction and watch the counter. For a 15-kilotonne yield you need about 2 × 10²⁴ fissions — starting from a single neutron, that's roughly 81 doublings. Here's the part that surprises everyone:
- At generation 70, the energy released so far is about 18 tonnes of TNT. Negligible on the scale of the final result.
- At generation 80, it's about 18 kilotonnes — essentially the whole thing.
The entire, city-destroying yield arrives in the last five doublings. For sixty-something generations it looks like almost nothing is happening, and then everything happens at once. With about 10 nanoseconds between generations, the whole event is over in under a millionth of a second — which is why, once it begins, there is no possibility of intervening. That "almost everything arrives at the very end" behaviour is a property of every exponential process, and it's worth sitting with well beyond nuclear physics: it's the same maths behind compound interest, viral spread, and runaway feedback of any kind.
Three designs, one principle
The third screen compares the two 1945 bomb designs and the later hydrogen bomb — as concept diagrams, showing the physical idea rather than any engineering.
The physics that separates the first two is a single idea: critical mass depends on density. Whether a chain reaction can sustain itself comes down to whether neutrons are more likely to hit another nucleus than to escape from the surface — and that depends on how tightly the nuclei are packed, not just on how much material there is.
- The gun-type design (Little Boy) brings two pieces of uranium together. Each alone is too small to sustain a reaction; combined, the assembly is large enough that neutrons find another nucleus before escaping. Simple, and wasteful — only about 1% of the uranium fissioned before the device blew itself apart.
- The implosion design (Trinity, then Fat Man) instead compresses a single sphere. Squeeze the same material into a smaller volume and its density rises, so neutrons travel less far between nuclei and fewer escape. A mass that was subcritical becomes supercritical without adding any material at all. This is far more efficient — Fat Man fissioned a much larger fraction of a much smaller core.
The hydrogen bomb adds a second stage where light nuclei fuse, triggered by the extreme temperature of a fission first stage. Fusion isn't limited by critical mass the way fission is, which is why yields jumped from kilotonnes to megatonnes. And the fusion reaction itself is the same deuterium–tritium physics students meet in the fusion simulator elsewhere in the suite — a nice moment where two topics connect.
There's also a satisfying bit of physics in why these devices are inefficient at all. Once the material is heated to millions of degrees it expands violently, its density drops, and the chain reaction stops. The reaction destroys the very conditions it needs to continue — which is exactly why the gun-type design wasted 99% of its fuel.
The fourth screen, and a sanity check on the numbers
The last screen is a yield comparison on a logarithmic scale, running from conventional explosives up through the 1945 bombs to the largest device ever tested — which released something like 3,300 times the energy of Hiroshima. A log scale is the only honest way to show that range on one chart, and it's a good incidental lesson in why we use log scales at all.
All the energy figures were checked against the physics before they went in: the mass–energy conversions, the fission counts (200 MeV per fission), the number of doublings required. When the tool tells you a 15-kilotonne yield needs about 81 generations, that's calculated, not asserted — and it's the same calculation a student would do by hand, just run instantly as you change the device.
Using it in class
- Lead with the gram. Open on the E = mc² screen and let the "less than a gram" number sit before you explain anything. It buys attention for the rest of the lesson.
- Separate the two masses explicitly. Mass converted versus fuel fissioned is the single most common misconception in this topic. The readouts show both — make students say which is which.
- Run the chain reaction and watch the counter, not the slider. The point isn't that k > 1 grows; it's how it grows. Pause at generation 70, note how little energy there is, then step to 80. The jump does the teaching.
- Tie fission and fusion together. When you reach the hydrogen bomb's second stage, jump back to the fusion simulator. Same D–T reaction, same binding-energy curve — students see the topic as connected rather than a list.
- Use the log scale deliberately. Ask why the yields can't be shown on a normal axis. It's a genuine maths point wearing a physics costume.
The whole thing scales up for projection — there's a zoom control in the corner, or full-screen the browser — and it sits alongside the reactor, fission/fusion and nucleus simulators, so the same E = mc² that runs the power station runs the weapon. That one equation covers both is, quietly, one of the more remarkable facts in the whole of physics.