IB Physics Mass–Energy Equivalence (E=mc²): FAQ

Start by finding the mass defect (Δm) — the difference between the total mass of the separate particles and the mass of the combined nucleus — then convert to energy using E = Δm c², or Δm × 931.5 MeV per unified mass unit. Show units at every step; examiners mark method, not just the final number.

Mass–energy equivalence is Einstein's result that mass and energy are two expressions of the same physical quantity, related by E = mc². In IB Physics it explains why nuclear reactions release such large amounts of energy: a tiny, measurable loss of mass converts into energy according to that formula, using the rest mass and the speed of light.

Mass defect (Δm) is the difference between the total mass of a nucleus's separate protons and neutrons and the actual, smaller mass of the bound nucleus. Binding energy is the energy equivalent of that missing mass, E = Δm c² — physically, the energy needed to pull the nucleus apart into free nucleons.

Both. Mass–energy equivalence itself — used for mass defect, binding energy, fission and fusion — is core content for SL and HL alike, in the nuclear physics sub-topics. Only the deeper treatment of E=mc² inside special relativity, including the relativistic energy–momentum relation, is additional HL-only content.

E=mc² appears across the nuclear physics sub-topics — radioactive decay (mass defect), fission and fusion (energy released per reaction) — and, for HL only, in special relativity, where it defines a particle's rest energy. It's genuinely cross-topic content examiners can draw on in almost any calculation question.

Binding energy per nucleon equals the total binding energy of a nucleus divided by its nucleon number A. Work out the mass defect, convert it to energy using 931.5 MeV per unified mass unit, then divide by A — the result shows how tightly bound (and stable) that nucleus is.

You need the unified mass unit conversion — 1 u = 931.5 MeV c⁻² (also 1 u = 1.661 × 10⁻²⁷ kg) — plus the rest masses of the proton, neutron and any relevant nuclides, all supplied in the IB Physics data booklet. You're never expected to memorise nuclide masses.

The most common error is subtracting the masses the wrong way round and ending up with a negative binding energy, or mixing atomic mass (which includes electrons) with nuclear mass without adjusting. Common mistake to check: always subtract the smaller, bound-nucleus mass from the larger, separate-particles mass so your answer comes out positive.

Show every step — masses used, the subtraction, the conversion factor, and the final answer with correct units and significant figures. Paper 2 extended-response questions award marks against explicit marking points, so an unexplained final answer, even if numerically correct, loses easy method marks.

Practise the same three-step calculation — find the masses, calculate the mass defect, convert to energy — until it's automatic, then move to past-paper questions combining it with fission, fusion or radioactive decay context. Timed practice catches the unit and sign errors that untimed revision usually hides.

Not conceptually — the formula itself is simple. It catches students out through multi-step arithmetic and unit conversion, not through difficult ideas. Most marks lost in mocks come from misplacing a decimal in 931.5 or mixing atomic and nuclear mass, rather than misunderstanding what mass defect actually means.

It can appear anywhere. Paper 1 multiple-choice questions test the concept and simple substitutions; Paper 2 extended-response questions ask for full multi-step calculations; Paper 3's data-based questions may hand you nuclide mass data to process. It's one of the more exam-paper-agnostic topics on the syllabus.

For the core nuclear physics content — mass defect, binding energy, fission and fusion — HL and SL students study exactly the same material and face similarly demanding calculations. The extra difficulty at HL comes from special relativity, where E=mc² reappears alongside the relativistic energy–momentum relation as genuinely new content.

IB Physics covers mass–energy equivalence to broadly similar depth as A-level — mass defect, binding energy, fission and fusion are common to both. The difference is that IB HL formally extends it into special relativity with the relativistic energy–momentum relation as compulsory content, which most A-level specifications don't require in the same way.