Calculator
Choose a mode, enter your known values, and calculate remaining material, required time, half-life, or activity with one page.
Decay Graph
The plotted curve updates from your calculated values when available. Otherwise, a sample decay trend is shown.
Example Data Table
| Isotope | Initial Amount | Half-Life | Elapsed Time | Remaining Amount |
|---|---|---|---|---|
| Iodine-131 | 100 g | 8 days | 16 days | 25 g |
| Carbon-14 | 50 mg | 5730 years | 11460 years | 12.5 mg |
| Technetium-99m | 200 MBq | 6 hours | 12 hours | 50 MBq |
| Phosphorus-32 | 80 units | 14.3 days | 28.6 days | 20 units |
Formula Used
Core decay equation
N(t) = N₀ e-λt
Here, N(t) is the remaining quantity after time t, N₀ is the initial quantity, and λ is the decay constant.
Half-life relationship
t½ = ln(2) / λ
The half-life is the time needed for half of the radioactive sample to remain. This relation lets you switch between half-life and decay constant.
Time for a target amount
t = ln(N₀ / N) / λ
Use this when you know the starting quantity, desired remaining quantity, and half-life, and want the exact time required.
Activity decay
A(t) = A₀ e-λt
Activity follows the same exponential law as mass or atom count, so the calculator also handles becquerel-based radioactive activity problems.
How to Use This Calculator
- Select the calculation mode that matches your chemistry problem.
- Choose the time unit you want to work with.
- Enter the known values in the visible fields.
- Pick graph sample points if you want a smoother curve.
- Press Calculate Now to show the result above the form.
- Review the summary cards and decay graph.
- Use the CSV or PDF buttons to export the result.
FAQs
1. What does half-life mean in chemistry?
Half-life is the time required for half of a radioactive sample to decay. It helps compare isotopes and predict how much material remains after any chosen period.
2. Why is radioactive decay exponential?
Each unstable nucleus has a constant probability of decaying over time. Because the rate depends on how many undecayed nuclei remain, the decrease follows an exponential pattern.
3. Can this calculator find half-life from observations?
Yes. Use the mode for finding half-life from known initial amount, final amount, and elapsed time. The calculator derives the decay constant first, then computes half-life.
4. Does activity decay the same way as mass?
Yes. Activity, atom count, and remaining mass all follow the same exponential decay law. Their values change proportionally for a given isotope and time period.
5. What units should I use for time?
Use any unit listed in the calculator, but stay consistent. If half-life is entered in days, the time value should also represent days for correct results.
6. What is the decay constant?
The decay constant, written as λ, measures how quickly a radioactive substance decays. Larger λ values mean faster decay and shorter half-lives.
7. What is mean lifetime?
Mean lifetime is the average time a radioactive nucleus exists before decaying. It equals 1 divided by the decay constant and is longer than half-life.
8. When is this calculator useful?
It is useful for chemistry homework, nuclear science practice, radiopharmaceutical timing, lab planning, isotope comparisons, and quickly checking decay-based estimates with exports and graphs.