Half-Life & Risk

Definition of Half-Life

The half-life of a radioactive isotope is the time taken for half of the unstable nuclei in a sample to decay. This means that after one half-life, only half of the original radioactive atoms remain undecayed.

Radioactive decay is an exponential decay process. This means the number of undecayed nuclei decreases by the same fraction (half) every half-life, not by a fixed amount.

The decay of each nucleus is random and unpredictable. We cannot say when a particular nucleus will decay, only the probability that it will decay over a certain time period.

Because of this randomness, the half-life is a statistical measure that applies to large numbers of atoms.

For example, if a sample has a half-life of 4 hours, after 4 hours half the nuclei will have decayed, after 8 hours a quarter remain, after 12 hours one eighth remain, and so on.

Mathematically, the number of undecayed nuclei N at time t can be calculated using the formula:
N = N₀ \times (1/2)^{t/T}, where N₀ is the initial number of nuclei, and T is the half-life.

Measuring Half-Life

Half-life can be measured by monitoring the count rate or decay rate of radiation emitted by a radioactive sample. The count rate is the number of radioactive emissions detected per second.

As the nuclei decay, the count rate decreases over time, following an exponential decay curve.

Plotting count rate against time on a graph produces a curve that falls steeply at first, then more slowly.

The half-life is estimated by finding the time interval over which the count rate halves.

For instance, if the count rate starts at 800 counts per second, and it takes 3 minutes to fall to 400 counts per second, the half-life is 3 minutes.

This method is commonly used in practical work and research to determine the half-life of unknown isotopes.

Example: A radioactive sample has a count rate of 1200 counts per second at time zero. After 5 minutes, the count rate is 600 counts per second. What is the half-life?

Since the count rate halves from 1200 to 600 in 5 minutes, the half-life is 5 minutes.

Radiation Risks

Radioactive emissions are ionising radiation. They can remove electrons from atoms and molecules, causing damage to living cells.

This damage can lead to mutations, cell death, or cancer. The risk depends on the type of radiation, its energy, and the level and duration of exposure.

Alpha particles are highly ionising but cannot penetrate skin; they are dangerous if ingested or inhaled.

Beta particles can penetrate skin but are stopped by a few millimetres of aluminium.

Gamma rays are weakly ionising but penetrate deeply and require thick lead or concrete shielding.

Short-term exposure to high doses of radiation can cause radiation sickness, burns, or death.

Long-term exposure to low doses increases the risk of cancer and genetic damage.

Risk is also affected by how close you are to the source and how long you are exposed.

Background Radiation & Risk

Background radiation is the low-level ionising radiation present naturally in the environment.

Sources include:

• Radon gas from rocks and soil
• Cosmic rays from space
• Radioactive isotopes in food, building materials, and the human body

Levels of background radiation vary depending on location, altitude, and local geology.

For example, people living in areas with granite rock may receive higher background doses due to radon.

In everyday life, background radiation poses a very low risk and is generally harmless.

Risk assessments consider the dose received and the potential health effects.

For comparison, a chest X-ray gives a dose roughly equivalent to a few days of background radiation.

Example: If a sample has a half-life of 2 hours, how many nuclei remain after 6 hours? After 3 half-lives (6 ÷ 2), the number remaining is (1/2)^3 = 1/8 of the original.