Half-Life Calculator
Calculate radioactive decay and remaining amounts
Calculate Decay
Results
Enter values to calculate radioactive decay
About Half-Life Calculator
Understanding radioactive decay and half-life calculations
Half-Life Calculator
Calculate radioactive decay and remaining amount after time elapsed. Essential for nuclear physics, chemistry, and environmental science.
How to Use Half-Life Calculator
1. Enter Initial Amount: Input the starting quantity of the substance
2. Enter Half-Life: Input the half-life period of the substance
3. Enter Time Elapsed: Input the time that has passed
4. Click "Calculate": Get instant results with decay information
5. View Results: See remaining amount and percentage decayed
Features
- Radioactive Decay: Calculate remaining amount after time elapsed
- Half-Life Period: Determine decay characteristics
- Percentage Remaining: See what portion remains
- Half-Lives Count: Number of half-life periods passed
- Scientific Applications: Perfect for physics and chemistry
- Educational: Learn about radioactive decay concepts
Half-Life Fundamentals
What is Half-Life?
Half-life is the time required for half of a radioactive substance to decay. It's a constant characteristic of each radioactive isotope.
Half-Life Formula
[ N(t) = N_0 imes left( rac{1}{2} ight)^{ rac{t}{t_{1/2}}} ]
Where:
- N(t) = remaining amount after time t
- N₀ = initial amount
- t = time elapsed
- t₁/₂ = half-life period
Common Half-Life Values
- Carbon-14: 5,730 years (radiocarbon dating)
- Uranium-238: 4.5 billion years (geological dating)
- Iodine-131: 8 days (medical applications)
- Radon-222: 3.8 days (environmental concerns)
Practical Applications
Archaeology and Geology
- Radiocarbon Dating: Determining age of organic materials
- Geological Dating: Age of rocks and fossils
- Climate Studies: Ice core and sediment analysis
- Evolution Research: Timeline of biological development
Medicine and Health
- Medical Imaging: Radioactive tracers and diagnostics
- Cancer Treatment: Radiotherapy planning
- Nuclear Medicine: Diagnostic procedures
- Radiation Safety: Exposure monitoring
Environmental Science
- Pollution Monitoring: Radioactive contamination tracking
- Nuclear Waste Management: Decay storage planning
- Environmental Protection: Radiation level assessment
- Disaster Response: Nuclear accident monitoring
Half-Life Examples
Example 1: Carbon-14 Dating
- Initial Amount: 100 units of Carbon-14
- Half-Life: 5,730 years
- Time Elapsed: 11,460 years
- Result: 25 units remaining (25% of original)
Example 2: Medical Isotope
- Initial Amount: 200 mCi of Iodine-131
- Half-Life: 8 days
- Time Elapsed: 24 days
- Result: 25 mCi remaining (12.5% of original)
Example 3: Nuclear Waste
- Initial Amount: 1000 kg of Plutonium-239
- Half-Life: 24,100 years
- Time Elapsed: 48,200 years
- Result: 250 kg remaining (25% of original)
Decay Process
Exponential Decay
Radioactive decay follows an exponential pattern:
- After 1 half-life: 50% remains
- After 2 half-lives: 25% remains
- After 3 half-lives: 12.5% remains
- After 4 half-lives: 6.25% remains
- After 5 half-lives: 3.125% remains
Decay Constant
The decay constant (λ) is related to half-life:
[ lambda = rac{ln(2)}{t_{1/2}} ]
Activity and Count Rate
The activity (A) of a radioactive substance:
[ A(t) = A_0 imes e^{-lambda t} ]
Types of Radioactive Decay
Alpha Decay
- Particle: Helium nucleus (2 protons, 2 neutrons)
- Penetration: Low (stopped by paper)
- Ionization: High
- Common Isotopes: Uranium-238, Radon-222
Beta Decay
- Particle: Electron or positron
- Penetration: Medium (stopped by aluminum)
- Ionization: Moderate
- Common Isotopes: Carbon-14, Strontium-90
Gamma Decay
- Particle: High-energy photon
- Penetration: High (requires dense shielding)
- Ionization: Low
- Common Isotopes: Cobalt-60, Iodine-131
Safety Considerations
Radiation Protection
- Time: Minimize exposure time
- Distance: Maximize distance from source
- Shielding: Use appropriate barriers
- Containment: Prevent contamination spread
Biological Effects
- Acute Effects: Radiation sickness at high doses
- Chronic Effects: Increased cancer risk
- Genetic Effects: DNA damage and mutations
- Threshold Levels: Safe exposure limits
Measurement Units
Activity Units
- Becquerel (Bq): 1 decay per second
- Curie (Ci): 3.7 × 10¹⁰ decays per second
- Counts Per Minute (cpm): Detector measurements
- Disintegrations Per Minute (dpm): Actual decay events
Dose Units
- Gray (Gy): Absorbed radiation dose
- Sievert (Sv): Effective biological dose
- Rad: Radiation absorbed dose (older unit)
- Rem: Roentgen equivalent man (older unit)
Tips for Half-Life Calculations
Common Mistakes to Avoid
- Unit Consistency: Ensure all time units match
- Negative Values: Time cannot be negative
- Zero Half-Life: Half-life must be greater than zero
- Exponent Errors: Use correct exponent in calculations
Practical Tips
- Scientific Notation: Use for very large/small numbers
- Logarithmic Scale: Useful for plotting decay curves
- Multiple Isotopes: Calculate each isotope separately
- Chain Decay: Consider daughter products in chains
Conclusion
Half-life calculations are fundamental to understanding radioactive decay processes. Whether you're dating archaeological artifacts, planning medical treatments, or managing nuclear waste, understanding half-life helps you predict and control radioactive processes. This calculator provides essential tools for half-life calculations, helping you work confidently with radioactive decay in scientific, medical, and environmental contexts.
Calculate radioactive decay and remaining amount after time elapsed. Essential for nuclear physics, chemistry, and environmental science.
How to Use Half-Life Calculator
1. Enter Initial Amount: Input the starting quantity of the substance
2. Enter Half-Life: Input the half-life period of the substance
3. Enter Time Elapsed: Input the time that has passed
4. Click "Calculate": Get instant results with decay information
5. View Results: See remaining amount and percentage decayed
Features
- Radioactive Decay: Calculate remaining amount after time elapsed
- Half-Life Period: Determine decay characteristics
- Percentage Remaining: See what portion remains
- Half-Lives Count: Number of half-life periods passed
- Scientific Applications: Perfect for physics and chemistry
- Educational: Learn about radioactive decay concepts
Half-Life Fundamentals
What is Half-Life?
Half-life is the time required for half of a radioactive substance to decay. It's a constant characteristic of each radioactive isotope.
Half-Life Formula
[ N(t) = N_0 imes left( rac{1}{2} ight)^{ rac{t}{t_{1/2}}} ]
Where:
- N(t) = remaining amount after time t
- N₀ = initial amount
- t = time elapsed
- t₁/₂ = half-life period
Common Half-Life Values
- Carbon-14: 5,730 years (radiocarbon dating)
- Uranium-238: 4.5 billion years (geological dating)
- Iodine-131: 8 days (medical applications)
- Radon-222: 3.8 days (environmental concerns)
Practical Applications
Archaeology and Geology
- Radiocarbon Dating: Determining age of organic materials
- Geological Dating: Age of rocks and fossils
- Climate Studies: Ice core and sediment analysis
- Evolution Research: Timeline of biological development
Medicine and Health
- Medical Imaging: Radioactive tracers and diagnostics
- Cancer Treatment: Radiotherapy planning
- Nuclear Medicine: Diagnostic procedures
- Radiation Safety: Exposure monitoring
Environmental Science
- Pollution Monitoring: Radioactive contamination tracking
- Nuclear Waste Management: Decay storage planning
- Environmental Protection: Radiation level assessment
- Disaster Response: Nuclear accident monitoring
Half-Life Examples
Example 1: Carbon-14 Dating
- Initial Amount: 100 units of Carbon-14
- Half-Life: 5,730 years
- Time Elapsed: 11,460 years
- Result: 25 units remaining (25% of original)
Example 2: Medical Isotope
- Initial Amount: 200 mCi of Iodine-131
- Half-Life: 8 days
- Time Elapsed: 24 days
- Result: 25 mCi remaining (12.5% of original)
Example 3: Nuclear Waste
- Initial Amount: 1000 kg of Plutonium-239
- Half-Life: 24,100 years
- Time Elapsed: 48,200 years
- Result: 250 kg remaining (25% of original)
Decay Process
Exponential Decay
Radioactive decay follows an exponential pattern:
- After 1 half-life: 50% remains
- After 2 half-lives: 25% remains
- After 3 half-lives: 12.5% remains
- After 4 half-lives: 6.25% remains
- After 5 half-lives: 3.125% remains
Decay Constant
The decay constant (λ) is related to half-life:
[ lambda = rac{ln(2)}{t_{1/2}} ]
Activity and Count Rate
The activity (A) of a radioactive substance:
[ A(t) = A_0 imes e^{-lambda t} ]
Types of Radioactive Decay
Alpha Decay
- Particle: Helium nucleus (2 protons, 2 neutrons)
- Penetration: Low (stopped by paper)
- Ionization: High
- Common Isotopes: Uranium-238, Radon-222
Beta Decay
- Particle: Electron or positron
- Penetration: Medium (stopped by aluminum)
- Ionization: Moderate
- Common Isotopes: Carbon-14, Strontium-90
Gamma Decay
- Particle: High-energy photon
- Penetration: High (requires dense shielding)
- Ionization: Low
- Common Isotopes: Cobalt-60, Iodine-131
Safety Considerations
Radiation Protection
- Time: Minimize exposure time
- Distance: Maximize distance from source
- Shielding: Use appropriate barriers
- Containment: Prevent contamination spread
Biological Effects
- Acute Effects: Radiation sickness at high doses
- Chronic Effects: Increased cancer risk
- Genetic Effects: DNA damage and mutations
- Threshold Levels: Safe exposure limits
Measurement Units
Activity Units
- Becquerel (Bq): 1 decay per second
- Curie (Ci): 3.7 × 10¹⁰ decays per second
- Counts Per Minute (cpm): Detector measurements
- Disintegrations Per Minute (dpm): Actual decay events
Dose Units
- Gray (Gy): Absorbed radiation dose
- Sievert (Sv): Effective biological dose
- Rad: Radiation absorbed dose (older unit)
- Rem: Roentgen equivalent man (older unit)
Tips for Half-Life Calculations
Common Mistakes to Avoid
- Unit Consistency: Ensure all time units match
- Negative Values: Time cannot be negative
- Zero Half-Life: Half-life must be greater than zero
- Exponent Errors: Use correct exponent in calculations
Practical Tips
- Scientific Notation: Use for very large/small numbers
- Logarithmic Scale: Useful for plotting decay curves
- Multiple Isotopes: Calculate each isotope separately
- Chain Decay: Consider daughter products in chains
Conclusion
Half-life calculations are fundamental to understanding radioactive decay processes. Whether you're dating archaeological artifacts, planning medical treatments, or managing nuclear waste, understanding half-life helps you predict and control radioactive processes. This calculator provides essential tools for half-life calculations, helping you work confidently with radioactive decay in scientific, medical, and environmental contexts.