Half-life is a core concept in nuclear chemistry and is essential for understanding radioactive decay, medical imaging, radiocarbon dating, and nuclear energy. In IB Chemistry, half-life appears in Topic 11 and Data Booklet reference tables. This article explains half-life clearly, shows how it works mathematically, and helps you apply it with confidence in exam questions.
What Is Half-Life?
Half-life (t½) is the time required for half of a radioactive substance to decay.
If you start with a certain number of radioactive nuclei, after one half-life:
- Half the nuclei have decayed
- Half remain undecayed
After another half-life, half of the remaining amount decays again.
This process continues in a predictable, exponential pattern.
Why Half-Life Is Important
Half-life tells us:
- How quickly a radioactive substance decays
- How long it remains hazardous
- How long it remains useful (e.g., medical tracers)
- How to calculate how much remains after a given time
- How to determine the age of ancient materials
IB questions often require applying half-life mathematically.
Radioactive Decay Is Exponential
Radioactive decay does not occur linearly.
Instead, the rate of decay is proportional to the number of undecayed nuclei remaining.
This leads to exponential behavior:
- After 1 half-life → 50% remains
- After 2 half-lives → 25% remains
- After 3 half-lives → 12.5% remains
- After n half-lives → (½)ⁿ remains
The pattern is predictable and consistent.
Half-Life Formula (IB Level)
To calculate the amount remaining after time t:
N = N₀ × (½)^(t / t½)
Where:
- N = amount remaining
- N₀ = original amount
- t = time passed
- t½ = half-life
This formula helps solve more advanced decay questions.
Worked Example (IB-Style)
A radioactive isotope has a half-life of 12 hours.
If you start with 40 g, how much remains after 36 hours?
Step 1: Determine the number of half-lives
36 ÷ 12 = 3 half-lives
Step 2: Apply the pattern
After 3 half-lives:
(½)³ = 1/8 remains
Step 3: Multiply
40 g × 1/8 = 5 g remain
This is a standard Paper 1 and Paper 2 calculation.
Graphs of Radioactive Decay
A half-life graph shows:
- Steep decline at first
- Gradual flattening over time
- Never reaches zero (asymptotic)
Axes:
- y-axis = number of nuclei, activity, or mass
- x-axis = time
These graphs illustrate exponential decay and are frequently tested in interpretation questions.
Measuring Half-Life
Half-life is measured experimentally by:
- Tracking activity (counts per second)
- Monitoring mass changes
- Measuring radiation intensity
- Following decay of medical tracers
Because decay is random at the atomic level but predictable statistically, half-life values are precise and characteristic of each isotope.
Real-World Applications
1. Radiocarbon Dating
C-14 half-life (5730 years) measures age of fossils and artifacts by comparing remaining C-14 to original levels.
2. Medical Imaging
Isotopes like Technetium-99m have short half-lives so patients are not exposed to long-term radiation.
3. Nuclear Waste Management
Understanding half-lives helps determine storage time needed before materials become safe.
4. Nuclear Power
Half-life influences fuel choice, safety protocols, and reactor design.
FAQs
Does a substance ever fully decay?
Not completely. Mathematically, it approaches zero but never fully reaches zero. Practically, it becomes negligible after many half-lives.
Why is decay random but predictable?
Individual nuclei decay randomly, but large populations behave predictably due to statistical averages.
Does half-life change with conditions?
No. Half-life is constant and unaffected by temperature, pressure, or chemical environment. It depends only on nuclear structure.
Conclusion
Half-life is the time required for half of a radioactive sample to decay. It is predictable, exponential, and essential for analyzing radioactive processes in IB Chemistry. By understanding how half-life works and mastering the formulas used to calculate decay, you gain the tools needed to interpret nuclear reactions, date materials, and understand real-world applications of radioactivity.
