Mass, Energy and the Unified Atomic Mass Unit
Mass and energy are one quantity written in two units, tied together by E = mc squared. On the nuclear scale that makes one atomic mass unit worth about 931 MeV, which is why nuclear energies dwarf chemical ones.
What a learner can do afterwards
- Converts a mass in kilograms or atomic mass units into an energy in joules and in MeV
- Compares the energy per particle from a nuclear change with that from a chemical one
- Explains why the change in mass goes unnoticed in everyday energy transfers
1 · Read
Mass and energy are one quantity in two units, tied by E equals m c squared, which is why a power station can run a city on barely any fuel. The c squared factor is huge: with c at 3.0e8 m/s, c squared is 9.0e16. Losing just 0.004 kg in a reaction releases 0.004 times 9.0e16, which is 3.6e14 J.
On the nuclear scale one atomic mass unit is worth about 931 MeV. A chemical change shuffles outer electrons and pays only a few eV per particle, like burning coal to heat a home. A nuclear change rebuilds the nucleus and pays millions of eV, roughly a million times more for each particle than coal.
The conversion runs both ways. Building a particle of mass 2.0e-28 kg from pure energy costs 2.0e-28 times 9.0e16, which is 1.8e-11 J. The formula only gives the exchange rate, not the machine that performs the swap.
Do not expect the scales to notice everyday transfers. Heating water adds energy, so its mass grows by E over c squared, but dividing by that enormous c squared leaves an unweighable speck. The change is real yet far too small for any balance.
Lost mass times c squared equals released energy, which is why nuclear changes dwarf chemical ones.
The rewritten readings were written for this dataset.
More to read
Rest mass and energy
Relativity relates rest mass to energy through E = mc². Because c² is enormous, a tiny decrease in total rest mass can release much energy. Stars and nuclear reactors use this process. Energy can also produce particles with mass. Mass contributes to a system's energy rather than being a separate conserved quantity.
Mass differences in nuclear reactions
Energy-releasing fission of heavy nuclei and fusion of light nuclei leave products with less total rest mass. The difference becomes kinetic energy and radiation. Per particle, releases can exceed chemical energy by factors of millions. Grams of uranium can supply more energy than tonnes of coal. Atomic mass units help track these masses.
Why speed matters in relativity
Speeding up increases an object's energy and the size of its momentum, but not its rest mass. Observers moving relative to one another can disagree about which events are simultaneous. Massive objects cannot reach the speed of light in a vacuum; their rest energy is E = mc². Relativistic effects depend on v/c. They are tiny at everyday speeds but matter in particle accelerators.
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