Short Answer
Half-life is the time required for half of the radioactive atoms in a sample to decay. It is a fixed and constant property of every radioactive element, meaning it does not change with temperature, pressure, or any physical condition. After one half-life, only half of the original amount of the substance remains.
Half-life helps scientists understand how quickly a radioactive substance becomes stable. It also helps in dating ancient objects, studying nuclear reactions, and calculating the safety period for radioactive materials. Every radioactive isotope has its own unique half-life.
Detailed Explanation :
Half-life
Half-life is a fundamental concept in nuclear physics that describes how long it takes for half of the atoms in a radioactive substance to undergo radioactive decay. Radioactive decay is a natural and spontaneous process in which an unstable atomic nucleus transforms into a more stable one by releasing particles or radiation. Because this decay happens randomly at the atomic level, it is impossible to predict when any single atom will decay. However, when dealing with large numbers of atoms, the decay follows a predictable pattern. This predictable rate is expressed through the half-life.
The half-life of a radioactive isotope is a unique and fixed property. It does not depend on environmental conditions such as temperature, pressure, or chemical reactions. It depends only on the internal structure of the nucleus. This makes half-life extremely useful for scientific calculations, dating techniques, and understanding nuclear processes.
Meaning of half-life
Half-life refers to the time it takes for half of the original radioactive atoms to disintegrate. After one half-life, only 50% of the substance remains. After two half-lives, 25% remains. After three half-lives, 12.5% remains, and so on. Although the amount decreases, the decay process never reaches zero; it just keeps reducing by half.
This gradual reduction follows an exponential decay pattern. Even though decay happens randomly to each individual atom, the overall behaviour of a sample is predictable.
Mathematical expression of half-life
The decay of radioactive substances is described by an exponential law. If N₀ is the initial number of atoms and N is the number remaining after time t, then:
where
- t = time elapsed
- T = half-life
This formula shows that the remaining quantity depends on how many half-lives have passed.
Examples of half-life values
Different radioactive isotopes have very different half-lives:
- Carbon-14: 5730 years (used in carbon dating)
- Iodine-131: 8 days (used in medical treatments)
- Uranium-238: 4.5 billion years (used to date rocks)
- Polonium-214: 0.000164 seconds
These values show that some isotopes decay very quickly, while others decay extremely slowly.
Importance of half-life in nuclear physics
Half-life is important because it allows scientists to:
- Predict how long a radioactive material will remain active
This is helpful in nuclear medicine, nuclear waste disposal, and radiation safety. - Understand nuclear stability
Isotopes with long half-lives decay slowly and are more stable.
Short half-lives indicate highly unstable nuclei. - Calculate energy released in nuclear reactions
The rate of decay determines how much energy is emitted over time.
Half-life and radioactivity levels
As radioactive atoms decay, the radioactivity (amount of radiation emitted) decreases with time. The activity of a radioactive sample is proportional to the number of undecayed atoms. After each half-life, both the number of atoms and the activity reduce by half.
For example:
- After 1 half-life → 50% activity
- After 2 half-lives → 25% activity
- After 3 half-lives → 12.5% activity
This relationship helps in planning safety measures and disposal of radioactive waste.
Half-life in medical applications
Many radioactive isotopes are used in diagnosis and treatment.
Examples:
- Iodine-131 (8 days) is used to treat thyroid disorders.
- Technetium-99m (6 hours) is used in medical imaging.
Short half-lives are preferred in medicine so the substance becomes harmless quickly after use.
Half-life in archaeology and geology
Carbon dating is one of the most famous applications of half-life. Carbon-14 decays with a half-life of 5730 years. When living organisms die, the amount of carbon-14 in their bodies decreases at a known rate. By measuring the remaining carbon-14, scientists can estimate the age of fossils up to about 50,000 years old.
For dating rocks and minerals, isotopes with long half-lives, such as uranium-238 or potassium-40, are used. These methods help determine the age of Earth and geological formations.
Half-life and nuclear waste
Radioactive waste from reactors remains dangerous for long periods. By knowing the half-lives of isotopes in the waste, scientists can estimate how many years it will take for the waste to decay to safe levels. Isotopes with short half-lives decay quickly and become safe sooner. Those with long half-lives remain hazardous for thousands of years.
Exponential and random nature
Although half-life is predictable mathematically, decay events are random. Any individual atom may decay early or very late, but the average behaviour of a large number of atoms always follows the same exponential decay pattern. This dual nature—random at atomic scale but predictable at large scale—is a key feature of radioactive decay.
Factors that do not affect half-life
It is important to note that half-life does not change with:
- pressure
- temperature
- chemical reactions
- physical state (solid, liquid, gas)
This consistency makes half-life a reliable scientific measure.
Conclusion
Half-life is the time required for half of the radioactive atoms in a sample to decay. It follows an exponential pattern and is a constant property of each radioactive isotope. Half-life helps in understanding nuclear stability, planning medical treatments, dating fossils and rocks, and ensuring safe handling of radioactive materials. It is a key concept that explains how radioactive substances change over time and how long they remain active.