Half-Life Calculator
Calculate radioactive decay, remaining quantity, and half-life for nuclear chemistry applications
Decay Results
Half-Life Results
Decay Time Results
Initial Quantity Results
Common Radioactive Isotopes
Understanding Radioactive Decay and Half-Life
Radioactive decay is a fundamental process in nuclear physics where unstable atomic nuclei lose energy by emitting radiation. The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to undergo decay.
Radioactive Decay Formula
N = N₀ × (1/2)t/t½
N = Quantity remaining after time t
N₀ = Initial quantity
t = Elapsed time
t½ = Half-life
Key Concepts in Radioactive Decay
Exponential Nature of Decay
Radioactive decay follows an exponential pattern, meaning the rate of decay is proportional to the number of remaining radioactive atoms. This results in a characteristic curve where the quantity decreases rapidly at first, then more slowly over time.
Decay Constant
The decay constant (λ) represents the probability that a nucleus will decay per unit time. It’s related to half-life by the formula:
λ = ln(2) / t½
Types of Radioactive Decay
- Alpha decay: Emission of alpha particles (helium nuclei)
- Beta decay: Conversion of neutrons to protons or vice versa
- Gamma decay: Emission of high-energy photons
- Electron capture: Absorption of an orbital electron by the nucleus
Practical Example: Carbon-14 Dating
Carbon-14 dating uses the known half-life of Carbon-14 (5730 years) to determine the age of organic materials. By measuring the ratio of Carbon-14 to Carbon-12 in a sample, scientists can calculate how long ago the organism died.
For example, if a sample contains 25% of its original Carbon-14, it has undergone two half-lives (50% → 25%), making it approximately 11,460 years old.
Applications of Half-Life Calculations
Archaeology and Geology
Radioactive dating techniques using isotopes like Carbon-14, Potassium-40, and Uranium-238 allow scientists to determine the age of artifacts, fossils, and geological formations with remarkable accuracy.
Medical Applications
Radioactive isotopes are used in medical diagnostics and treatment. Understanding their half-lives is crucial for:
- Determining appropriate dosages for radiation therapy
- Planning imaging procedures using radioactive tracers
- Ensuring patient safety by managing radiation exposure
Nuclear Energy and Safety
Half-life calculations are essential in nuclear power generation for:
- Predicting fuel consumption rates
- Managing radioactive waste storage and disposal
- Assessing environmental impact and safety protocols
Environmental Science
Radioactive tracers help scientists study environmental processes, including:
- Ocean current patterns
- Groundwater movement
- Atmospheric circulation
- Pollution tracking
Factors Affecting Radioactive Decay
Nuclear Stability
The half-life of a radioactive isotope is determined by the stability of its nucleus. Elements with unstable proton-neutron ratios tend to have shorter half-lives as they seek more stable configurations.
Environmental Conditions
Unlike chemical reactions, radioactive decay rates are generally unaffected by:
- Temperature changes
- Pressure variations
- Chemical bonding
- Physical state (solid, liquid, gas)
Quantum Tunneling
Radioactive decay involves quantum mechanical phenomena where particles “tunnel” through energy barriers that would be insurmountable according to classical physics. This probabilistic nature is what gives decay its random character while maintaining predictable statistical behavior for large numbers of atoms.
Frequently Asked Questions
Under normal conditions, the half-life of a radioactive substance is constant and cannot be altered by external factors like temperature, pressure, or chemical environment. However, in extreme conditions such as inside stars or particle accelerators, nuclear reactions can change decay rates.
After one half-life, approximately 50% of the original radioactive atoms remain. After two half-lives, about 25% remain, after three half-lives 12.5%, and so on. Theoretically, a radioactive substance never completely decays to zero.
Half-life depends on the specific nuclear structure of each isotope. Factors include:
- Proton-to-neutron ratio
- Nuclear binding energy
- Quantum mechanical properties
- Type of decay process
Scientists measure half-life by:
- Monitoring radiation intensity over time
- Counting decay events using Geiger counters or scintillation detectors
- Using mass spectrometry to measure isotope ratios
- Applying statistical analysis to decay data