E = mc² (Einstein 1905): even a tiny mass m converts
to energy E. One atomic mass unit u = 931.5 MeV/c². The mass defect Δm
of a nucleus is the difference between free nucleon masses and the
actual nucleus mass — entirely converted to binding energy.
About Mass–Energy Equivalence E=mc²
This simulation visualises Einstein's mass–energy relation E=mc², which says that mass and energy are interchangeable. It animates the two nuclear processes that exploit it — fission of a heavy nucleus and fusion of light nuclei — and plots the binding-energy-per-nucleon curve. The energy released equals the mass defect Δm times c², converted using the unit relation 1 atomic mass unit = 931.494 MeV/c².
Three mode buttons switch between Fission, Fusion and the B/A Curve. A speed slider sets the animation rate, while in fission mode a Trigger button and a critical-mass slider start a branching chain reaction. Live statistics report Δm, the energy in MeV, the binding energy per nucleon and the chain generation. The same physics powers nuclear reactors, stellar cores and weapons, making it one of the most consequential equations ever written.
Frequently Asked Questions
What does this simulation actually show?
It demonstrates Einstein's E=mc² through three views: animated nuclear fission of uranium-235, deuterium–tritium fusion, and a graph of binding energy per nucleon versus mass number. Each view illustrates how a small mass defect is released as a large amount of energy.
What is the mass defect Δm?
The mass defect is the difference between the combined mass of the free nucleons and the actual mass of the bound nucleus. That missing mass has been converted into the binding energy that holds the nucleus together. In a reaction, the change in Δm between reactants and products determines the energy released.
How is the energy calculated from the mass?
The simulation uses the conversion 1 atomic mass unit (u) equals 931.494 MeV/c². So you multiply the mass defect in atomic mass units by 931.494 to get the energy in MeV. For example, fission of U-235 has Δm ≈ 0.186 u, giving about 173 MeV per event.
What do the Fission, Fusion and B/A Curve buttons do?
Fission animates a U-235 nucleus absorbing a neutron and splitting into Barium-141 and Krypton-92 plus neutrons. Fusion shows deuterium and tritium merging into Helium-4 plus a neutron. The B/A Curve plots binding energy per nucleon against mass number, with Iron-56 marked at the peak.
What does the chain reaction Trigger and critical-mass slider do?
In fission mode the Trigger button releases a starting neutron into a cluster of U-235 nuclei. Each split emits two to three new neutrons that can strike further nuclei, producing successive generations. The critical-mass slider represents how readily the reaction sustains itself, mirroring the idea of a critical mass needed for a self-sustaining chain.
Why is Iron-56 special on the binding-energy curve?
Iron-56 sits at the peak of the binding-energy-per-nucleon curve at roughly 8.79 MeV per nucleon, making it among the most tightly bound and stable nuclei. Nuclei heavier than iron release energy by fission, while lighter nuclei release energy by fusion. The curve therefore explains why both processes are energetically favourable.
Is the energy released physically accurate?
The quoted values are realistic. U-235 fission releases about 173 MeV in the prompt products shown, D-T fusion releases 17.6 MeV, and the binding-energy data approximate measured values from the semi-empirical mass formula. The animations are schematic for clarity, but the masses, energies and unit conversions reflect genuine nuclear physics.
Why does fusion release less energy per event yet matter so much?
A single D-T fusion yields 17.6 MeV against fission's 173 MeV, but fusion releases far more energy per unit mass of fuel, the fuel (hydrogen isotopes) is abundant, and it leaves no long-lived radioactive waste. Its drawback is that nuclei must overcome electrostatic repulsion, requiring temperatures above 100 million kelvin.
Why is the speed of light squared so important in E=mc²?
Because c is about 300,000 km/s, c² is an enormous number. Multiplying even a tiny mass by c² gives a vast energy, which is why converting a fraction of a gram of mass yields the output of a power station. The squared term is what makes nuclear processes so much more energetic than chemical ones.
What real-world applications rely on this physics?
Nuclear reactors harness controlled fission chain reactions for electricity, while stars including the Sun shine by fusing hydrogen into helium. Fusion research aims to reproduce stellar power on Earth, and the same equations underpin radiometric dating, medical isotopes and nuclear weapons.