Fission and Fusion Sim for NCEA 2 and 3 Physics

 

Splitting and joining: a fission and fusion simulator for NCEA Physics

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Here's a puzzle to open a lesson with. Splitting a heavy atom releases energy. Joining light atoms also releases energy. But splitting and joining are opposites — so how can doing a thing and undoing it both give energy out? Something has to be wrong with the question.

Nothing is. Both really do release energy, and the reason they can is one of the most elegant ideas in the whole of physics — it all comes down to a single curve. This simulator lets students run both reactions, see the energy come out of each, and then meet the curve that explains why. And on the fusion side it goes further than most classroom tools, showing not just that fusion releases energy but why it's so fiendishly hard to make happen.

It's a single self-contained web page: open it in a browser, put it on the projector, and it runs. Below I'll walk through the physics across its two reactions, then flag some ways to use it.

Fission: splitting the heavy nucleus

The first tab is fission. A slow-moving neutron drifts into a uranium-235 nucleus and is absorbed. That makes the nucleus unstable — you can watch it wobble and deform — and then it splits, here into barium-141 and krypton-92, flinging out three fast neutrons in the process.

Two things are worth drawing students' attention to. First, those three neutrons are the seed of a chain reaction: each one can go on to split another nucleus, which is the entire basis of both reactors and weapons. Second, and this is the key point, the products weigh less than what you started with. Add up the mass before — neutron plus uranium — and the mass after — barium plus krypton plus three neutrons — and there's a shortfall. That missing mass is the mass defect, and it hasn't disappeared; it's been converted into energy via E = mc².

The simulator's mass–energy ledger does this calculation live. It shows the mass before, the mass after, the difference in atomic mass units and in kilograms, and then the energy that difference corresponds to — about 173 MeV for this single fission, counting up in front of you in both joules and MeV. It's E = Δmc² turned into a running total, using the real atomic masses.

Fusion: joining the light nuclei — and why it's hard

The second tab is fusion, and it's where the tool does something classroom simulations often skip. It's easy to say "fusion joins two light nuclei and releases energy." It's much more useful to show why nature fights it so hard — because that difficulty is the reason we have working reactors splitting atoms but not yet joining them at scale.

The reaction is deuterium plus tritium — the two heavy isotopes of hydrogen — combining to make helium-4 and a neutron. But both nuclei are positively charged, and like charges repel. To get them close enough for the strong force to snap them together, they have to be hurled at each other hard enough to overcome that electrostatic repulsion — the Coulomb barrier. In the simulator you can see the repulsion pushing back as the nuclei approach, and there's a temperature slider: below about 100 million kelvin, the nuclei don't have enough energy, they're repelled, and they bounce apart without fusing. Only when you crank the temperature high enough do they finally overcome the barrier, fuse, and release their energy.

That's already a better picture than most students get. But the tool then adds the two ingredients that separate a physics demonstration from an actual reactor, through a Lawson criterion panel.

Getting one pair of nuclei to fuse isn't a power station. For a self-sustaining burn you need three things at once, and the tool gives you a dial for each:

• Temperature — enough to get individual nuclei over the Coulomb barrier.
• Density — enough nuclei packed together that collisions happen often.
• Confinement time — the plasma has to hold its heat long enough, rather than leaking it to the walls, for fusion to keep going.

Multiply those three together and you get the triple product, and there's a threshold it has to clear — the Lawson criterion. The panel computes it live, along with the probability that any given nucleus actually fuses under the conditions you've set. The lesson that emerges is genuinely hard-won: you can have a plasma hot enough to fuse, but if it's too thin or too leaky, the burn dies out anyway. Fusion is difficult not because of any one obstacle but because you have to satisfy all three conditions simultaneously.

There's a nice visible contrast with fission built into this. Fission needs no such barrier — the neutron that triggers it is uncharged, so it wanders into the nucleus with no repulsion to overcome. That's exactly why fission was harnessed decades before fusion, and why fission can sustain a chain reaction so readily. The tool lets you feel that asymmetry rather than just be told it.

The curve that explains both

Now back to the opening puzzle. How can splitting and joining both release energy? The answer is the binding energy per nucleon curve, and the simulator draws it, updating to highlight whichever reaction you're running.

The curve plots how tightly bound each nucleon is, against the size of the nucleus. It rises steeply from the light elements, peaks at iron-56, and then declines slowly through the heavy elements. Iron sits at the top — it's the most tightly bound, the most stable nucleus there is.

Everything follows from that shape. Any reaction that moves nuclei towards iron increases the binding energy per nucleon, and the difference is released as energy. There are two ways to move towards the peak:

• From the right, split a heavy nucleus like uranium into medium-sized fragments — that's fission, sliding down the right-hand slope towards iron.
• From the left, fuse light nuclei like hydrogen into heavier ones — that's fusion, climbing the steep left-hand slope towards iron.

So splitting and joining aren't really opposites in the way the opening puzzle implied. They're both journeys towards iron, from opposite ends. That's the single idea that dissolves the paradox, and once students see the curve, the whole topic clicks into a shape they can hold in their head.

The curve also explains a quantitative fact the tool highlights: fusion releases several times more energy per nucleon than fission, because the left-hand slope is so much steeper than the gentle right-hand decline. Per kilogram of fuel, fusion is the far bigger prize — which is a large part of why so much effort goes into chasing it despite the difficulty.

A note on the numbers

The energy figures come from real atomic masses: about 173 MeV per fission of uranium-235, about 17.6 MeV per deuterium–tritium fusion. The mass–energy ledger runs the actual E = Δmc² arithmetic that a student would do by hand, just instantly. On the fusion side, the temperature threshold and the Lawson triple product use the standard values from fusion physics, so the "too thin or too leaky and it fails" behaviour is the real constraint, not a dramatisation.

One honest caveat: the fusion reactivity used to compute the probability is a good approximation in the 10–20 keV range the sliders cover, but it overstates the rate at very low temperatures, where real fusion collapses much faster due to quantum tunnelling probabilities. So treat the low-temperature percentages as illustrative rather than literal — fine for the concept, worth a word if a sharp student asks.

Using it in class

• Open with the paradox. Ask how splitting and joining can both release energy before you show the curve. Let them sit with the puzzle, then resolve it.
• Run both reactions, then reveal the curve. Do fission, do fusion, note that both release energy — then bring up the binding energy curve as the "aha," with iron at the peak explaining both.
• Make fusion fail first. On the fusion tab, start with the temperature too low so the nuclei bounce apart. The failure is the lesson — it shows the Coulomb barrier is real before you show it being overcome.
• Turn the Lawson dials one at a time. Get a plasma hot enough to fuse, then starve it of density or confinement and watch the burn die anyway. "All three at once" is the insight, and you can only feel it by breaking each condition in turn.
• Compare energy per nucleon, not per reaction. Fission's 173 MeV looks bigger than fusion's 17.6 MeV — until you divide by the number of nucleons involved. That division is where fusion's real advantage shows up.

It sits alongside the rest of the AS91172 suite, so the uranium nucleus splitting here is the same one that jiggles in the nucleus simulator and drives the reactor, and the deuterium–tritium fusion is the same reaction that powers the second stage of a hydrogen bomb. Start with a puzzle that seems to break the rules, and let one curve put it right.

Nuclear Weapons sim for NCEA 2 and 3 Physics

 

Less than a gram: a nuclear weapons physics simulator for NCEA Physics

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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.