Radioactive Decay Table- All Elements Decay Constants and Half-Lives
What Is a Radioactive Decay Table?
A radioactive decay table is a reference that lists all radioactive elements, their decay constants, and their half-lives. Scientists use these tables to predict how quickly atoms will break down over time.
You will find decay tables in nuclear physics, chemistry, medicine, and geology. If you work with any radioactive material, you need this data.
Decay Constant Explained
The decay constant (λ) tells you the probability that a single atom will decay in one second. A higher decay constant means faster decay.
Units are per second (s⁻¹). Some elements have decay constants so small they barely decay at all. Others are gone in fractions of a second.
How to Calculate Decay Constant
The formula is straightforward:
λ = ln(2) / t½
Where t½ is the half-life. You need natural logarithm of 2, which equals approximately 0.693.
Half-Life: The Basics
Half-life (t½) is the time it takes for half of the atoms in a sample to decay. After one half-life, you have 50% remaining. After two half-lives, 25%. After three, 12.5%.
Half-lives range from fractions of a second to billions of years. Uranium-238 has a half-life of 4.5 billion years. Polonium-212 decays in 0.3 microseconds.
The Relationship Between Decay Constant and Half-Life
These two values are inversely related. The equation is:
t½ = 0.693 / λ
Or rearranged:
λ = 0.693 / t½
This means if you know one, you can find the other. No need to memorize both — just remember the relationship.
Complete Radioactive Decay Table: Key Elements
Here are the most commonly referenced radioactive elements with their decay constants and half-lives:
| Element | Isotope | Half-Life | Decay Constant (s⁻¹) | Decay Type |
|---|---|---|---|---|
| Uranium | U-238 | 4.468 × 10⁹ years | 4.916 × 10⁻¹⁸ | Alpha |
| Uranium | U-235 | 7.04 × 10⁸ years | 3.12 × 10⁻¹⁷ | Alpha |
| Thorium | Th-232 | 1.40 × 10¹⁰ years | 1.57 × 10⁻¹⁸ | Alpha |
| Potassium | K-40 | 1.25 × 10⁹ years | 1.75 × 10⁻¹⁷ | Beta+ |
| Carbon | C-14 | 5,730 years | 3.83 × 10⁻¹² | Beta |
| Radium | Ra-226 | 1,600 years | 1.37 × 10⁻¹¹ | Alpha |
| Polonium | Po-210 | 138.4 days | 5.79 × 10⁻⁸ | Alpha |
| Cesium | Cs-137 | 30.17 years | 7.28 × 10⁻¹⁰ | Beta |
| Strontium | Sr-90 | 28.8 years | 7.62 × 10⁻¹⁰ | Beta |
| Cobalt | Co-60 | 5.27 years | 4.17 × 10⁻⁹ | Beta |
| Tritium | H-3 | 12.32 years | 1.78 × 10⁻⁹ | Beta |
| Americium | Am-241 | 432.2 years | 5.08 × 10⁻¹¹ | Alpha |
| Polonium | Po-212 | 0.299 µs | 2.32 × 10⁶ | Alpha |
| Fermium | Fm-257 | 100 days | 8.02 × 10⁻⁸ | Alpha |
How to Read a Decay Table
Reading these tables is simple once you know what to look for.
- Isotope column tells you which specific form of the element
- Half-life tells you how long until half the sample is gone
- Decay constant gives you the probability rate per second
- Decay type shows how the atom breaks apart (alpha, beta, gamma)
Getting Started: Calculate Decay for Any Element
Here is a practical method to calculate remaining activity after any time period.
Step 1: Gather Your Data
Find the half-life of your element from the table above. Convert everything to consistent units. Use seconds for the decay constant calculation.
Step 2: Calculate the Decay Constant
Divide 0.693 by the half-life in seconds.
Example: Carbon-14 has a half-life of 5,730 years.
5,730 years × 86,400 seconds/day × 365.25 days/year = 180,947,736,000 seconds
λ = 0.693 / 180,947,736,000 = 3.83 × 10⁻¹² s⁻¹
Step 3: Apply the Decay Equation
Use this formula:
N(t) = N₀ × e^(-λt)
Where N(t) is remaining atoms, N₀ is initial atoms, λ is decay constant, and t is elapsed time in seconds.
Step 4: Calculate Activity if Needed
Activity (A) = λ × N(t)
Activity is measured in Becquerel (decays per second) or Curie (3.7 × 10¹⁰ decays per second).
Why This Data Matters
Geologists use C-14 dating to determine the age of organic remains up to 50,000 years old. Nuclear engineers need decay constants to design safe containment for waste that remains dangerous for thousands of years. Medical physicists calculate dosages for radiation therapy using these exact values.
Without accurate decay tables, none of this would work.
Common Mistakes to Avoid
- Mixing time units — always convert half-life to seconds before calculating λ
- Confusing activity with number of atoms — they are different measurements
- Forgetting that decay is probabilistic — individual atoms are random, but large samples follow predictable patterns
- Using the wrong isotope — elements often have multiple radioactive isotopes with completely different half-lives
Where to Find Complete Decay Data
The table above covers common elements, but hundreds of radioactive isotopes exist. For comprehensive data, check:
- National Nuclear Data Center (NNDC)
- International Atomic Energy Agency (IAEA) databases
- Chart of the Nuclides published by Oak Ridge National Laboratory
These sources update their decay data as measurements improve. Values in reference books sometimes differ slightly from the most recent measurements.
The Bottom Line
Radioactive decay tables give you two interconnected values: half-life and decay constant. Pick whichever is easier for your calculation and derive the other using 0.693 as the conversion factor.
For quick reference, memorize the relationship. For accuracy, use verified databases. The math is simple. The applications are everywhere.