Does ΔE = c²Δm apply only to nuclear reactions?

No. It applies to all energy changes, but the mass change is only measurable in nuclear reactions.

What is the atomic mass unit, u?

One twelfth of the mass of a carbon-12 atom, 1.661 × 10⁻²⁷ kg.

The total mass of the separate nucleons minus the mass of the nucleus.

Define binding energy.

The minimum energy needed to separate a nucleus into its individual protons and neutrons.

How do you calculate binding energy from the mass defect?

Binding energy = mass defect in u × 931.5 MeV (or c²Δm with the mass in kg).

What is binding energy per nucleon?

The binding energy of a nucleus divided by its nucleon number; it shows how tightly bound the nucleus is.

Which nucleus is most stable on the binding energy per nucleon curve?

Iron-56, with about 8.8 MeV per nucleon.

Why does fusion of light nuclei release energy?

The product has a higher binding energy per nucleon, so the total mass decreases and the difference is released as energy.

Why does fission of heavy nuclei release energy?

The fragments have a higher binding energy per nucleon than the original nucleus, so the mass decreases and energy is released.

Why would fusing two nuclei heavier than iron-56 not release energy?

The product would have a lower binding energy per nucleon, so energy would have to be supplied.

Mass, energy and binding energyAQA A-Level Physics: Flashcards

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What does ΔE = c²Δm mean?

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What does ΔE = c²Δm mean?: Any change in the energy of a system is accompanied by a change in its mass; the energy change equals c² times the mass change.
Does ΔE = c²Δm apply only to nuclear reactions?: No. It applies to all energy changes, but the mass change is only measurable in nuclear reactions.
What is the atomic mass unit, u?: One twelfth of the mass of a carbon-12 atom, 1.661 × 10⁻²⁷ kg.
What is the energy equivalent of 1 u?: 931.5 MeV.
How many joules in 1 MeV?: 1.60 × 10⁻¹³ J.
Define mass defect.: The total mass of the separate nucleons minus the mass of the nucleus.
Define binding energy.: The minimum energy needed to separate a nucleus into its individual protons and neutrons.
How do you calculate binding energy from the mass defect?: Binding energy = mass defect in u × 931.5 MeV (or c²Δm with the mass in kg).
What is binding energy per nucleon?: The binding energy of a nucleus divided by its nucleon number; it shows how tightly bound the nucleus is.
Which nucleus is most stable on the binding energy per nucleon curve?: Iron-56, with about 8.8 MeV per nucleon.
Why does fusion of light nuclei release energy?: The product has a higher binding energy per nucleon, so the total mass decreases and the difference is released as energy.
Why does fission of heavy nuclei release energy?: The fragments have a higher binding energy per nucleon than the original nucleus, so the mass decreases and energy is released.
Why would fusing two nuclei heavier than iron-56 not release energy?: The product would have a lower binding energy per nucleon, so energy would have to be supplied.

Exam questions on Mass, energy and binding energy

A student is analysing the helium-4 nucleus using these data: nuclear mass of helium-4 = 4.00151 u; mass of a proton = 1.00728 u; mass of a neutron = 1.00867 u; 1 u = 931.5 MeV.
Explain why the mass of a helium-4 nucleus is less than the total mass of its separate nucleons.2 marks
A power station burns coal. Burning 1.0 kg of coal releases 3.0 × 10⁷ J of energy. The speed of light in a vacuum is c = 3.00 × 10⁸ m s⁻¹.
Suggest why the mass change in a chemical reaction is never noticed, but the mass change in a nuclear reaction can be measured.2 marks
Average binding energy per nucleon: hydrogen-2 (deuterium) 1.1 MeV; helium-4 7.1 MeV; iron-56 8.8 MeV; uranium-235 7.6 MeV. When a uranium-235 nucleus undergoes fission, the fragments formed have an average binding energy per nucleon of 8.5 MeV. 1 MeV = 1.60 × 10⁻¹³ J.
Explain, in terms of binding energy per nucleon, why energy is released both when light nuclei such as hydrogen-2 fuse and when heavy nuclei such as uranium-235 undergo fission.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).