Half-Life Calculator
What is Half-Life?
Half-Life ($t_{1/2}$) is the time required for a quantity to reduce to exactly half of its initial value. It is the standard unit used to describe Exponential Decay.
Imagine you have a cup of coffee. The caffeine doesn't leave your body all at once. It fades gradually. If caffeine has a half-life of 5 hours:
- 0 Hours: 100% remains.
- 5 Hours: 50% remains.
- 10 Hours: 25% remains.
- 15 Hours: 12.5% remains.
This process continues infinitely, getting closer to zero but never theoretically touching it.
The Decay Formula
To calculate the remaining amount without waiting, we use this equation:
- N(t): Quantity remaining at time t.
- N₀: Initial Quantity.
- t: Time elapsed.
- t½: The Half-Life of the substance.
Application 1: Carbon Dating
How do archaeologists know a dinosaur bone is 65 million years old?
They use the half-life of Carbon-14 (5,730 years). All living things breathe in Carbon-14. When they die, they stop breathing, and the Carbon-14 begins to decay into Nitrogen.
By measuring how much Carbon-14 is left in a bone compared to a living sample, scientists can calculate exactly how long ago the creature died.
Application 2: Medical Drugs
Doctors use half-life to determine dosing schedules. If a painkiller has a very short half-life (2 hours), you need to take it often (every 4-6 hours). If it has a long half-life (24 hours), you only take it once a day.
It typically takes 5 half-lives for a drug to be completely eliminated from your body (97% gone).
Example: Caffeine (5 hour half-life) takes about 25 hours to fully leave your system.
Famous Isotopes and their Half-Lives
Half-lives vary from fractions of a second to billions of years.
| Isotope | Half-Life | Use Case |
|---|---|---|
| Polonium-214 | 0.00016 seconds | Nuclear Physics |
| Iodine-131 | 8 Days | Thyroid Cancer Treatment |
| Carbon-14 | 5,730 Years | Carbon Dating Fossils |
| Plutonium-239 | 24,100 Years | Nuclear Waste (Chernobyl) |
| Uranium-238 | 4.5 Billion Years | Dating the age of the Earth |