Nuclear energy for OCR A-level Physics
This page covers the following topics:
1. Nuclear energy calculations
2. The atomic mass unit
3. Nuclear energy release
4. Average binding energy
5. Nuclear power safety
Energy and mass are equivalent. This is summarised in Einstein's famous equation: E = mc², where E is energy in Joules, m is mass in kg and c is the speed of light (3 × 10⁸ m/s). The mass of a nucleus has been found to be less than the combined mass of all the nucleons. This difference in mass is known as the mass defect. The mass defect arises due to the fact that some of the mass of the nucleons being converted into energy to hold the nucleus together, as by the equivalence of mass and energy. Using the mass defect in Einstein's equation gives the binding energy of the nucleus.
The relative atomic mass is the ratio of the average mass of one atom of an element to one twelfth of the mass of an atom of carbon-12. The atomic mass unit is given by u, where u = 1.66 × 10⁻²⁷ kg. This value can be calculated by dividing the mass of a carbon atom by 12.
Einstein's equation and the mass difference between the elements before and after the nuclear reaction can be used to calculate the energy released in fusion and fission.
Nuclei require energy to be held together, due to the repulsive forces between the protons in them. This energy is called the binding energy. Binding energy is the energy required to break up a nucleus or the energy released when the nucleus is formed by the joining of separate nucleons. The binding energy per nucleon is the energy required to remove each nucleon. A higher binding energy per nucleon represents a more stable nuclei, as more energy will be required to break it up.
There are benefits and risks associated with nuclear power. Nuclear power plants do not take up a lot of space, do not produce a lot of waste and they do not contribute to carbon emissions, thus do not contribute to landfill and global warming. Nuclear power plants also don't emit smoke particles, thus do not contribute to acid rain. Moreover, a lot of nuclear energy can be produced from a small amount of fuel. Nuclear power is also reliable, since it doesn't depend on weather. However, disposing of nuclear waste is dangerous to the environment, thus doing it is expensive. There is also always the risk of nuclear accidents, which can lead to people being exposed to harmful radiation.
Use the given graph to deduce whether helium or uranium have more stable nuclei.
The binding energy per nucleon of uranium is much higher than that for helium, meaning that uranium nuclei are more stable than helium nuclei.
Are there any geographical limitations associated with nuclear power?
Nuclear power plants do not require a lot of space, thus there aren't many geographical limitations associated with nuclear power.
The atomic mass unit of an oxygen atom is 16u. Calculate its mass in kg.
Mass = 16 × 1.66 × 10⁻²⁷ kg = 2.656 × 10⁻²⁶ kg.
Use the given table to calculate the energy release in the following fusion reaction: ³₁H + ²₁H → ⁴₂He + ¹₀n.
Mass defect = (5.007 + 3.343 − 1.675 − 6.645) × 10⁻²⁷ kg = 0.03 × 10⁻²⁷ kg. Using E = mc², E = 0.03 × 10⁻²⁷ kg × (3 × 10⁸ m/s)² = 2.7 × 10⁻¹² J.
Sketch a graph of binding energy per nucleon against the mass number.
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