(b) energy released (or absorbed) in simple nuclear reactions

The idea

In simple nuclear reactions, energy released or absorbed is determined by the change in total rest mass between reactants and products, using E = Δmc². To find Δm, subtract the total product mass from the total reactant mass. A positive Δm means mass has decreased, so energy is released (e.g., in deuterium-tritium fusion). A negative Δm means mass has increased, indicating energy is absorbed; this absorbed energy is converted into the increased rest mass of the products. When calculating, convert masses in unified atomic mass units (u) to kilograms before using c = 3.00 × 10⁸ m s⁻¹, or use the conversion 1 u = 931.5 MeV directly.

What earns the marks

• State that the energy change is proportional to the change in rest mass, using E = Δmc².
• Calculate Δm by subtracting the total product mass from the total reactant mass.
• Interpret a positive Δm (mass decrease) as energy released and a negative Δm (mass increase) as energy absorbed to create rest mass.
• Convert mass in u to kg using 1 u = 1.66 × 10⁻²⁷ kg, or use 1 u = 931.5 MeV, before finding the final energy.
• Give the energy in joules or MeV with an appropriate unit and sensible significant figures.

Common mistakes and how to put them right

• Subtracting reactant mass from product mass but treating a negative result as energy released.

  Put it right: Define Δm as reactant mass minus product mass so a positive value indicates a release.

• Using E = mc² with the total mass of the reactants rather than the mass difference.

  Put it right: Use only Δm, the change in mass.

• Mixing units by inserting a mass in u directly into E = Δmc² with c in m s⁻¹.

  Put it right: Convert u to kg first or to use the MeV equivalent of 1 u.

• Assuming absorbed energy increases the kinetic energy of the products.

  Put it right: Recognise that absorbed energy primarily increases the rest mass of the products.

Exam tips

• Write the balanced nuclear equation before doing any arithmetic so every reactant and product is counted.
• Keep full calculator precision through the mass subtraction and round only the final energy.
• Check the sign of Δm against whether the question says energy is released or absorbed.