Radioactive decay - waves and particles Revision Notes

What is Half-Life? (Higher)

Half-life is defined as the time it takes for the number of radioactive nuclei in a sample to halve, or for the activity of the sample to halve. It is a characteristic property of each radioactive isotope and is not affected by external conditions. For example, if a sample has a half-life of 5 days, after 5 days, half of the original radioactive atoms will have decayed. After another 5 days (a total of 10 days), half of the remaining half will have decayed, meaning a quarter of the original remains.

Calculating Remaining Fraction (Higher)

To find the fraction of a radioactive substance remaining after a certain number of half-lives (n), use the formula: Remaining fraction = (1/2)^n. For example, after 3 half-lives, the fraction remaining is (1/2)^3 = 1/8. This formula can be applied to the number of atoms, mass of the substance, or its activity, as they are all proportional to the number of radioactive nuclei present.

Calculating Net Decline Ratio (Higher)

The net decline refers to the proportion of the original radioactive nuclei that have decayed. If the fraction remaining after 'n' half-lives is (1/2)^n, then the fraction that has decayed is 1 - (1/2)^n. To express this as a ratio, let 'R' be the remaining fraction and 'D' be the decayed fraction. The ratio of decayed nuclei to original nuclei is D:1. For instance, if 1/8 remains, then 7/8 has decayed. The net decline expressed as a ratio to the original amount is 7:8.

Example Calculation (Higher)

Consider a radioactive isotope that undergoes 4 half-lives. First, calculate the fraction remaining: (1/2)^4 = 1/16. Next, calculate the fraction that has decayed: 1 - 1/16 = 15/16. Finally, express the net decline as a ratio of decayed nuclei to original nuclei: 15:16. This means for every 16 original nuclei, 15 have decayed.

Electron Arrangement in Atoms

Electrons in an atom are not randomly distributed but occupy distinct energy levels or shells, often visualised as orbits around the nucleus. Each shell corresponds to a specific energy value; electrons closer to the nucleus are in lower energy shells, and those further away are in higher energy shells. The number of electrons in each shell is limited, and atoms tend to have their lowest energy shells filled first. This organised arrangement is fundamental to an atom's stability and reactivity. The outermost electrons, known as valence electrons, are particularly important as they determine the atom's chemical behaviour and its ability to form bonds with other atoms.

Changes in Electron Energy Levels

The electron arrangement within an atom is not static and can change when the atom interacts with electromagnetic radiation. When an atom absorbs electromagnetic radiation, electrons can gain energy and move from a lower energy shell to a higher energy shell, moving further from the nucleus. This transition results in the atom being in an 'excited state'. Excited states are unstable, and electrons will eventually return to lower energy shells. As they drop back to a lower energy level, they emit electromagnetic radiation in the form of a photon. The energy of the absorbed or emitted photon is precisely equal to the energy difference between the two electron shells involved in the transition. This principle is key to understanding atomic spectra.

Ionisation: Forming Ions

An atom is typically electrically neutral, containing an equal number of protons (positive charge) and electrons (negative charge). However, an atom can become an ion by gaining or losing electrons. Specifically, if an atom loses one or more of its outermost electrons, it disrupts its charge balance. The atom will then have more positively charged protons than negatively charged electrons, resulting in a net positive charge. This positively charged particle is called a positive ion. The process of losing electrons is called ionisation. The energy required to remove an electron from an atom is known as ionisation energy. Ionisation is a critical process in many contexts, including the behaviour of gases in electric fields and the interaction of radiation with matter.

Understanding Half-Life

Half-life is the time it takes for the number of radioactive nuclei in a sample to halve, or for the activity of the sample to halve. This is a fundamental property of each radioactive isotope. For example, if a substance has a half-life of one hour, after one hour its activity will be half of its initial value. After two hours, it will be a quarter, and after three hours, an eighth, and so on. The decay is exponential, meaning it never reaches zero activity, but the hazard level can become negligible over a sufficiently long time.

Hazards of Short Half-Life Isotopes

Radioactive materials with a short half-life decay very quickly. This means they emit a large amount of radiation over a short period. This high initial activity makes them extremely hazardous in the immediate term, as intense exposure can cause severe damage. However, due to their rapid decay, their activity falls to safe levels relatively quickly. This characteristic makes them useful for applications where exposure needs to be limited, like some medical tracers, but requires careful handling during their active phase.

Hazards of Long Half-Life Isotopes

Isotopes with a long half-life decay slowly. While their rate of radiation emission (activity) might be relatively low at any given moment compared to a short-lived, equally active source, they remain radioactive and hazardous for extended periods, potentially thousands to millions of years. This prolonged hazard poses significant challenges for safe storage and disposal, as they can cause long-term environmental contamination and chronic exposure risks to living organisms over many generations. Nuclear waste is a prime example of this type of material.

Connecting Half-Life to Hazard Management

The half-life of a radioactive material dictates the necessary safety precautions and disposal methods. Short half-life sources demand immediate, robust shielding and controlled handling due to high initial intensity but are easier to manage in the long term once decayed. Long half-life sources require secure, long-term containment solutions to prevent environmental release and protect against chronic exposure for millennia, even if their instantaneous activity is lower. Understanding half-life is crucial for assessing radioactive risk.

Unstable Nuclei and Radioactive Decay

Atomic nuclei are made of protons and neutrons. Some nuclei are unstable; this instability often arises from an unfavourable ratio of neutrons to protons or simply an excess of energy. To become more stable, these nuclei undergo radioactive decay, a spontaneous process where they emit particles or energy. The particles emitted are commonly alpha (helium nuclei), beta (fast-moving electrons or positrons), or gamma (high-energy electromagnetic waves) radiation. Each type of radiation carries energy and can affect surrounding matter by transferring this energy, leading to ionisation.

Nuclear Fission and Energy Release

Nuclear fission is a process where a large, unstable nucleus, such as Uranium-235, splits into two or more smaller nuclei. This splitting is typically initiated by absorbing a neutron. When fission occurs, a substantial amount of energy is released. This energy is released as kinetic energy of the fission products and neutrons, and as gamma radiation. This energy release is due to a small amount of mass being converted into energy according to Einstein's mass-energy equivalence principle, though this specific formula is not needed at this level. The fission process also typically releases two or three additional neutrons.

Chain Reactions

The neutrons released during a fission event can go on to strike other unstable nuclei, causing them to undergo fission too. If, on average, more than one of the released neutrons causes a further fission, then the number of fission events will increase exponentially. This escalating sequence of fission events is known as a chain reaction. A chain reaction can be controlled, as in nuclear reactors where control rods absorb excess neutrons to maintain a steady rate of energy production. Alternatively, an uncontrolled chain reaction can lead to a very rapid and immense release of energy, such as in nuclear weapons. Understanding and controlling chain reactions is crucial for both safe nuclear energy and preventing uncontrolled explosions.