Nuclear physics studies the structure, stability, and transformations of atomic nuclei. This cheat sheet helps students track nuclear symbols, balance decay equations, and connect radioactive decay to measurable quantities. It is especially useful for solving half-life, activity, binding energy, and reaction energy problems in grade 11 and 12 physics.
The most important ideas are conservation of nucleon number, conservation of charge, and exponential decay. Radioactive samples follow , with half-life given by . Nuclear energy calculations use mass defect and Einstein’s relation , often expressed using .
Key Facts
- A nuclide is written as , where is the mass number, is the atomic number, and the number of neutrons is .
- In every nuclear reaction, total mass number and total atomic number are conserved, so and .
- Alpha decay emits , so a parent nucleus changes according to .
- Beta-minus decay emits an electron and an antineutrino, so .
- Beta-plus decay emits a positron and a neutrino, so .
- Radioactive decay follows , where is the number of undecayed nuclei, is the initial number, and is the decay constant.
- Half-life and decay constant are related by , and after half-lives the remaining amount is .
- Nuclear binding energy is found from , where the mass defect is .
Vocabulary
- Nuclide
- A specific nucleus identified by its number of protons and total nucleons .
- Isotope
- Atoms of the same element with the same but different neutron numbers .
- Half-life
- The time required for half of the radioactive nuclei in a sample to decay.
- Activity
- The decay rate of a radioactive sample, given by .
- Mass defect
- The missing mass between separate nucleons and the actual nucleus, converted into binding energy.
- Binding energy
- The energy required to completely separate a nucleus into individual protons and neutrons.
Common Mistakes to Avoid
- Forgetting to conserve both and is wrong because nuclear equations must balance nucleon number and charge separately.
- Confusing half-life with decay constant is wrong because is a time while is a probability per unit time, related by .
- Using linear subtraction for radioactive decay is wrong because radioactive decay is exponential, so the correct model is or .
- Treating gamma emission as a change in atomic number is wrong because gamma decay releases energy but leaves and unchanged.
- Using atomic masses without checking electrons is wrong because mass defect calculations require consistent masses, either all nuclear masses or correctly balanced atomic masses.
Practice Questions
- 1 Complete the alpha decay equation: .
- 2 A sample has nuclei and a half-life of . How many nuclei remain after ?
- 3 A radioactive isotope has and nuclei. Find its activity using .
- 4 Explain why nuclei with higher binding energy per nucleon are generally more stable than nuclei with lower binding energy per nucleon.
Understanding Nuclear Physics & Radioactivity
A nucleus is held together by the strong nuclear force. This force is extremely powerful at very short distances, but it acts only across the tiny width of a nucleus. Protons repel each other electrically, so larger nuclei need enough neutrons to add strong-force attraction without adding more electric repulsion.
The balance is not perfect in many nuclei. An unstable nucleus can change into a more stable arrangement by emitting radiation. In beta minus decay, a neutron changes into a proton inside the nucleus.
In beta plus decay, a proton changes into a neutron. Gamma radiation is different. It occurs when a nucleus has excess energy after another nuclear change and releases that energy as a high-energy photon.
Individual decay events are random. No one can predict when one particular nucleus will decay. A large sample behaves predictably because it contains an enormous number of nuclei.
This is why half-life is useful. It describes the rate at which a whole population decreases, not a deadline for each atom. Activity measures how many decays happen each second.
One becquerel means one decay per second. A detector does not always record every decay.
Its reading can depend on distance, shielding, detector efficiency, and natural background radiation. In experiments, background counts should be measured and subtracted before comparing sources.
Binding energy explains why both fusion and fission can release energy. Nuclei near iron have a high binding energy per nucleon, meaning their nucleons are held especially tightly. Light nuclei can release energy by joining together and moving closer to this stable region.
This is fusion, which powers stars. Very heavy nuclei can release energy by splitting into medium-sized nuclei. This is fission, used in nuclear reactors.
The released energy comes from a small decrease in total mass. It appears mainly as kinetic energy of particles and radiation.
A chain reaction occurs when neutrons from one fission can trigger further fissions. Reactors control this process by absorbing some neutrons and removing heat.
When solving nuclear equations, first identify what kind of decay is taking place from the changes in proton number and mass number. Then check both totals separately. Do not treat mass number as ordinary mass.
It counts nucleons. For binding energy questions, be careful about whether the data use nuclear masses or atomic masses. Atomic masses include electrons, so the chosen particle masses must match the given data.
Unit conversion matters because atomic mass units are tiny while nuclear energies are often given in megaelectronvolts. These ideas matter beyond textbook problems.
Radioactive tracers help doctors image organs, radiation can treat some cancers, and radiometric dating estimates the ages of rocks. Every use requires careful control because radiation can damage living tissue when exposure is too high.