Radioactivity Calculator
Calculate radioactivity decay, half-life, and activity instantly. Determine remaining amount after decay, calculate decay time, and convert between activity units (Becquerel and Curie). Perfect for nuclear chemistry, medical physics, and laboratory work.
Edited by Gail Joyce
Gail Joyce reviews chemistry calculator pages for formula clarity, scope consistency, and cleaner routing between related problem types.
This page is maintained as a focused chemistry workflow tool. Inputs, units, and supporting guidance are reviewed so routine calculations stay practical and easy to verify.
Radioactivity Calculator
Calculate radioactivity decay, remaining amount, half-life, and activity. Supports calculations for any radionuclide using exponential decay equations. Activity can be calculated in Becquerel (Bq) or Curie (Ci).
Table of Contents
Quickly navigate to different sections of this guide.
Understanding Radioactivity
Radioactivity is the spontaneous decay of unstable atomic nuclei, transforming them into more stable forms. This process releases energy in the form of radiation—alpha particles, beta particles, or gamma rays. Every radioactive isotope has a characteristic half-life, the time required for half of a sample to decay. This fundamental property makes radioactivity predictable and measurable, enabling applications from medical imaging to archaeological dating.
Why does radioactivity matter? Understanding radioactive decay is crucial for nuclear medicine, where isotopes like technetium-99m (half-life: 6 hours) are used for diagnostic imaging. Archaeologists use carbon-14 dating (half-life: 5,730 years) to determine the age of ancient artifacts. Nuclear power plants rely on precise decay calculations for safety and fuel management. Our Radioactivity Calculator simplifies these complex calculations, handling exponential decay equations automatically.
Radioactive decay follows exponential decay, described by the equation N(t) = N₀ × e^(-λt), where N₀ is the initial amount, λ is the decay constant, and t is time. The decay constant relates to half-life through λ = ln(2) / t₁/₂ ≈ 0.693 / t₁/₂. Activity, measured in Becquerel (Bq) or Curie (Ci), represents the rate of decay—the number of nuclei decaying per second. Our Radioactivity Calculator handles all these calculations, converting between units and providing step-by-step explanations.
Common Radioactivity Units
Half-life: time required for half of a radioactive sample to decay. It can range from fractions of a second to billions of years.
Decay constant (λ): probability of decay per unit time. It relates to half-life by λ = ln(2) / t₁/₂.
Activity: decay rate of a sample, measured in Becquerel (Bq) or Curie (Ci), where 1 Ci = 3.7 × 10¹⁰ Bq.
How to Use the Radioactivity Calculator
Choose the decay relationship you want to solve, then enter the values required for that mode only.
- Select the calculation type: Choose remaining amount, decay time, half-life from decay constant, or activity.
- Enter the known values: Add the starting amount, half-life, elapsed time, remaining amount, or decay constant depending on the question you are solving.
- Keep time units aligned: Use the same basis for half-life, elapsed time, and decay constant so the decay equations stay consistent.
- Review the result and steps: The calculator shows the solved quantity together with the exponential-decay relationship used, which makes lab checks and homework verification easier.
Important Notes
- • Radioactive decay is exponential, so equal half-life intervals remove the same fraction, not the same absolute amount.
- • Activity depends on both the decay constant and the number of nuclei present at that moment.
- • 1 Curie equals 3.7 × 10¹⁰ Becquerel, so convert carefully when checking older references.
- • Scientific notation is helpful for very large nucleus counts and very small decay constants.
Formulas and Equations
The calculator uses the standard exponential-decay relationships from nuclear chemistry.
Remaining Amount
Use this form when the half-life is known and you want to find the fraction or amount remaining after a given time.
Decay Constant and Half-Life
The decay constant gives the probability of decay per unit time and connects directly to half-life.
Activity
Activity is the decay rate of the sample and is commonly reported in Bq or converted to Ci.
Worked Examples
Short examples showing how common radioactivity calculations are solved.
Example 1: Remaining Carbon-14 After Two Half-Lives
Scenario: A sample starts with 100 units of carbon-14. How much remains after 11,460 years if the half-life is 5,730 years?
Solution:
11,460 years equals two half-lives.
N(t) = 100 × (1/2)² = 25
Answer: 25% of the original sample remains.
Example 2: Time Needed to Reach 12.5%
Scenario: Iodine-131 has a half-life of 8 days. How long does it take for a sample to reach 12.5% of its initial amount?
Solution:
12.5% = 1/8 = (1/2)³, so the sample passes through three half-lives.
Time = 3 × 8 days = 24 days
Answer: It takes 24 days.
Example 3: Activity From Decay Constant
Scenario: A sample contains 2.0 × 10¹² nuclei and has a decay constant of 3.0 × 10⁻⁶ s⁻¹. What is the activity?
Solution:
A = λN
A = (3.0 × 10⁻⁶ s⁻¹)(2.0 × 10¹²) = 6.0 × 10⁶ s⁻¹
Answer: The activity is 6.0 × 10⁶ Bq.
Frequently Asked Questions (FAQs)
Common questions about radioactive decay, half-life, and activity calculations.
What is radioactivity and half-life?
Radioactivity is the spontaneous decay of unstable atomic nuclei. Half-life is the time required for half of a sample to decay, and it is fixed for each radionuclide.
How do I calculate the remaining amount after decay?
Use N(t) = N₀ × (1/2)^(t/t₁/₂) or the equivalent exponential form N(t) = N₀ × e^(-λt), where λ is the decay constant.
What is the relationship between half-life and decay constant?
They are related by λ = ln(2) / t₁/₂. A larger decay constant means faster decay and a shorter half-life.
How is activity calculated?
Activity is A = λ × N, where λ is the decay constant and N is the number of radioactive nuclei present at that moment.
What units are used for radioactivity?
Activity is typically reported in Becquerel (Bq) or Curie (Ci). Half-life can be expressed in seconds, minutes, hours, days, or years.
References and Further Reading
For more information about radioactive decay, half-life, and activity:
| Resource | Description | Category |
|---|---|---|
| IAEA Nucleus | International Atomic Energy Agency reference data for radionuclides and decay information | Official |
| U.S. NRC | Plain-language explanation of radioactive decay, half-life, and activity concepts | Regulatory |
| OpenStax Chemistry 2e | General chemistry reference for nuclear chemistry and radioactive decay calculations | Textbook |