Nuclear fission and fusion, the conservation of mass-energy, and the calculation of the energy released using the mass difference and $E = mc^2$.

What this key area is asking

The SQA wants you to describe nuclear fission and fusion, state that mass and energy together are conserved, and calculate the energy released in a nuclear reaction from the mass difference using $E = mc^2$.

Fission and fusion

In fission, a nucleus such as uranium-235 absorbs a slow neutron, becomes unstable and splits. The released neutrons can trigger further fissions, giving a chain reaction that, when controlled, powers a nuclear reactor. In fusion, light nuclei such as deuterium and tritium are forced together at extremely high temperatures and pressures; this is the process that powers the Sun and the stars.

Conservation of mass-energy and E = mc^2

In a nuclear reaction the total mass before is slightly greater than the total mass after. The difference is the mass defect, and it does not vanish: it is converted into energy. Mass and energy are two forms of the same thing, linked by Einstein's relationship.

The key to every calculation is to find the difference between the total mass of the reactants and the total mass of the products, then multiply by $c^2$. Because $c^2 = 9.0 \times 10^{16}\ \text{m}^2 \text{s}^{-2}$, even a mass defect of a few $10^{-28}\ \text{kg}$ releases picojoules of energy per reaction, which is vast on the nuclear scale.

Examples in context

Nuclear power stations use a controlled fission chain reaction in uranium or plutonium to boil water and drive turbines; control rods absorb neutrons to keep the chain reaction steady. The Sun shines by fusing hydrogen into helium in its core, converting about four million tonnes of mass into energy every second. Experimental reactors such as ITER aim to harness fusion on Earth, which would give a near-limitless, low-waste energy source if the engineering of confining a hot plasma can be solved. Nuclear weapons release the same mass-energy uncontrolled. In every case the energy comes from a small loss of mass multiplied by the huge factor $c^2$.

Try this

Q1. State the difference between nuclear fission and nuclear fusion. [2 marks]

• Cue. Fission splits a heavy nucleus into smaller nuclei; fusion joins light nuclei into a heavier one.

Q2. A reaction loses $2.0 \times 10^{-28}\ \text{kg}$ of mass. Calculate the energy released. Take $c = 3.0 \times 10^{8}\ \text{m s}^{-1}$. [3 marks]

• Cue. $E = mc^2 = 2.0 \times 10^{-28} \times 9.0 \times 10^{16} = 1.8 \times 10^{-11}\ \text{J}$.

Q3. Explain why nuclear reactions release so much more energy than chemical reactions for the same mass of fuel. [1 mark]

• Cue. A measurable mass is converted to energy through $E = mc^2$, and the factor $c^2$ is enormous, whereas chemical reactions only rearrange electrons.