Half-life: The Clock of Radioactive Decay
What Exactly is Half-life?
Imagine you have a large bag of 1,000 popping candy pieces. Every minute, exactly half of the remaining pieces pop. After one minute, 500 pieces are left. After another minute, 250 remain. This is the core idea behind half-life. In radioactive materials, the "popping" is the spontaneous transformation of an unstable nucleus into a more stable one, a process called radioactive decay. The half-life $(t_{1/2})$ is the time it takes for half of the radioactive atoms in a sample to undergo this decay.
It is also the time for the sample's activity (or count rate) to halve. Activity measures how many decays occur per second. So, if a Geiger counter clicks 400 times per minute near a sample, after one half-life, it will click about 200 times per minute.
A Step-by-Step Look at a Half-life Decay
Let's trace the decay of a hypothetical element, "Unobtanium-300", which has a half-life of 1 day. We start with 16,000 atoms.
| Number of Half-lives | Time Elapsed (days) | Atoms Remaining | Fraction Remaining |
|---|---|---|---|
| 0 | 0 | 16,000 | 1/1 |
| 1 | 1 | 8,000 | 1/2 |
| 2 | 2 | 4,000 | 1/4 |
| 3 | 3 | 2,000 | 1/8 |
| 4 | 4 | 1,000 | 1/16 |
Notice that after each half-life, the number of atoms is halved. It doesn't matter if you start with 16,000, 1,600, or 16 atoms; half of them will decay in the same fixed time period. This table also shows that the sample never truly reaches zero; it just gets closer and closer, which is a key feature of exponential decay.
The Immense Range of Half-lives in Nature
Half-lives are a fixed property of each radioactive isotope[1] and they vary enormously. Some materials decay in fractions of a second, while others take billions of years. This variety is what makes different isotopes useful for different purposes.
| Isotope | Half-life | Common Use |
|---|---|---|
| Polonium-214 | 0.000164 seconds | Smoke detectors |
| Iodine-131 | 8.02 days | Medical treatment and diagnosis |
| Cobalt-60 | 5.27 years | Cancer radiation therapy |
| Carbon-14 | 5,730 years | Dating organic artifacts (carbon dating) |
| Uranium-238 | 4.47 billion years | Dating the age of the Earth |
Half-life in Action: Real-World Applications
The concept of half-life is not just a theoretical idea; it has powerful and practical applications that affect our daily lives and understanding of the world.
Radiometric Dating: This is one of the most famous uses. Scientists can determine the age of an object by measuring the amount of a radioactive isotope left in it and comparing it to the amount of its stable decay product. For example, living organisms constantly exchange carbon with the atmosphere, maintaining a steady level of Carbon-14. When they die, this exchange stops, and the C-14 begins to decay. By measuring the remaining C-14 and knowing its half-life (5,730 years), we can estimate how long ago the organism died. This is how we date ancient wooden tools, mummies, and fossils.
Medical Uses: In nuclear medicine, radioactive tracers with short half-lives are introduced into the body. Iodine-131 (half-life 8 days) is used to diagnose and treat thyroid conditions because the thyroid gland naturally absorbs iodine. The radiation helps destroy malfunctioning cells, and the short half-life ensures the radioactivity doesn't stay in the patient's body for long.
Nuclear Energy and Safety: Understanding half-life is critical for handling nuclear waste. Waste products from nuclear reactors have a wide range of half-lives. Some need to be isolated for a few years, while others must be stored securely for thousands of years. The half-life tells us how long a material will remain dangerously radioactive.
Common Mistakes and Important Questions
Q: Can you predict when a specific atom will decay?
A: No, this is a common point of confusion. Radioactive decay is a random process at the level of a single atom. We have no way of knowing if a particular uranium atom will decay in the next second or in a million years. The half-life is a statistical average that only becomes highly predictable when dealing with a very large number of atoms.
Q: Does half-life change if the conditions change (e.g., temperature or pressure)?
A: For nearly all practical purposes, no. The half-life of a radioactive isotope is generally constant and is not affected by external factors like temperature, pressure, or chemical bonding. This constancy is what makes it so reliable for applications like radiometric dating.
Q: After two half-lives, is the sample completely gone?
A: No. After one half-life, 50% remains. After two half-lives, half of that 50% decays, leaving 25% of the original sample. The amount never reaches zero; it just keeps halving, approaching closer and closer to zero. This is why we say it takes 10 half-lives for a sample to be considered effectively gone (only about 0.1% remains).
Footnote
[1] Isotope: Atoms of the same element that have the same number of protons but different numbers of neutrons. For example, Carbon-12 (stable) and Carbon-14 (radioactive) are both carbon, but C-14 has two extra neutrons, making it unstable.