A nuclear fission reaction releases a large amount of energy. A student says: 'Mass was destroyed and converted into energy.' What is wrong with this description?
ANothing is wrong — mass is destroyed and energy is created in nuclear reactions
BMass is not involved at all — nuclear energy comes from releasing stored electromagnetic potential energy
CMass and energy are the same thing; the rest energy decreased and kinetic energy increased, but total energy is conserved — mass was not 'destroyed'
DThe description is imprecise but harmless; no energy is actually released, only redistributed among particles
The phrase 'mass destroyed and converted into energy' implies mass and energy are separate things that can be interconverted. But E = mc² says they are the same thing in different units. In fission, the total rest mass of the products is less than the reactants (mass defect), because some rest energy has become kinetic energy of the fragments. No energy is created or destroyed — it is already conserved throughout. The right frame is: rest energy decreased, kinetic energy increased, total energy unchanged.
Question 2 Multiple Choice
A photon has zero rest mass. Using the full relativistic energy-momentum relation E² = (pc)² + (mc²)², what is the energy of a photon with momentum p?
AE = 0, because a massless particle has no rest energy and therefore no total energy
BE = mc² still applies, with m interpreted as the photon's effective mass
CE = pc — the mc² term vanishes, leaving only the momentum contribution
DE = γmc², but with γ → ∞ as v → c, so the energy is formally infinite
Setting m = 0 in E² = (pc)² + (mc²)² gives E² = (pc)², so E = pc. This is consistent with the photon relation E = hf and p = hf/c, which gives pc = hf = E. The expression E = γmc² is indeterminate for photons (both γ and m diverge/vanish), which is why the full energy-momentum relation is the correct starting point. The full relation is Lorentz-invariant and covers both massive and massless particles.
Question 3 True / False
The equation E = mc² applies only to objects at rest; for a moving object, the correct expression for its total energy is E = γmc².
TTrue
FFalse
Answer: True
E = mc² (or E₀ = mc²) is specifically the rest energy — the energy a particle has when v = 0 and γ = 1. The total relativistic energy of a moving particle is E = γmc², where γ = 1/√(1 − v²/c²) > 1 whenever v > 0. E = mc² is a special case of E = γmc² with v = 0. This is not a flaw in E = mc²; it correctly describes the enormous energy content of mass even at rest.
Question 4 True / False
In matter-antimatter annihilation, mass is destroyed and energy is created from very little, which is why the process seems to violate conservation of mass.
TTrue
FFalse
Answer: False
Mass-energy equivalence means mass is not a separately conserved quantity — energy is. When an electron and positron annihilate to produce two gamma rays, the rest energy of both particles (2 × 511 keV = 1.022 MeV) is entirely converted to photon energy. Total energy is conserved throughout. There is no 'creation from nothing.' The apparent violation of 'mass conservation' is simply because mass conservation is not the correct law — energy conservation (which includes rest energy) is.
Question 5 Short Answer
What is the mass defect of a nucleus, and how does it provide direct experimental evidence for E = mc²?
Think about your answer, then reveal below.
Model answer: The mass defect is the difference between the mass of a nucleus and the sum of the masses of its constituent protons and neutrons. A helium-4 nucleus, for example, is lighter than two free protons plus two free neutrons. This missing mass corresponds exactly to the binding energy of the nucleus via E = Δmc² — the energy required to pull the nucleus apart into its components. Measuring both the mass defect (with a mass spectrometer) and the binding energy (from nuclear reaction energetics) and verifying E = Δmc² is a direct, quantitative confirmation of mass-energy equivalence.
The mass defect is one of the clearest experimental confirmations of E = mc². It shows that binding energy has mass — the bound system weighs less because some of the constituent rest energy was released as binding energy when the nucleus formed. This effect is tiny for chemical bonds (far too small to measure) but large enough to measure precisely in nuclear physics (about 0.7% for helium-4). It also explains why nuclear fuel releases millions of times more energy than chemical fuel per kilogram.