Example Data Table
| Sample | Initial Amount | Half Life | Elapsed Time | Expected Remaining |
|---|---|---|---|---|
| Radioisotope A | 100 g | 8 hours | 16 hours | 25 g |
| First order reactant | 2 mol | 5 days | 10 days | 0.5 mol |
| Tracer activity | 400 Bq | 3 years | 9 years | 50 Bq |
Formula Used
The calculator uses the first order exponential decay model.
A(t) = A0 e-kt
A(t) = A0(1/2)t / t1/2
k = ln(2) / t1/2
t1/2 = ln(2) / k
t = ln(A0 / A) / k
A0 is the starting amount. A(t) is the amount after time t. k is the decay constant. t1/2 is the half life.
How to Use This Calculator
Select the value you want to calculate. Enter all known values in matching units. Use the same time unit for half life, elapsed time, and decay constant. Leave unknown fields blank when they are not needed. Press Calculate to view the result. Use CSV or PDF export for records.
Understanding Half Life Exponential Decay
Why Exponential Decay Matters
Half life is a simple idea with wide chemistry value. A sample does not lose a fixed mass each hour. It loses a fixed fraction during each equal half life period. This pattern is called exponential decay. It describes radioactive isotopes, unstable compounds, tracer studies, and first order reactions. The curve falls quickly at first. Later, the change becomes smaller, because less material remains.
What The Calculator Measures
This calculator connects the main decay variables. You can solve for remaining amount, original amount, half life, elapsed time, or decay constant. The same page also shows percent remaining, percent decayed, number of half lives, and mean lifetime. These values help compare samples that use different time units or starting amounts. They also help check laboratory notes before reports are written.
Chemistry Use Cases
In radiochemistry, half life helps estimate activity after storage. In kinetics, the same equation can model a first order reactant. In environmental chemistry, it can describe pollutant loss when removal follows first order behavior. In pharmaceutical work, it can show how concentration declines with time. Always confirm that the process truly follows first order decay before using the result for decisions.
Reading The Output
A large decay constant means a fast loss rate. A short half life also means fast decay. The remaining fraction shows what part of the original sample is still present. The decayed percent shows how much has disappeared or transformed. Mean lifetime equals one divided by the decay constant. It is useful for comparing decay models, but it is not the same as half life.
Good Practice
Use consistent time units. Enter positive values only. Do not mix hours and days in the same calculation. For isotope safety, use official activity data and approved procedures. For reaction studies, compare the calculated half life with experimental plots. If measurements are noisy, repeat the calculation with high and low estimates. This gives a practical range for uncertainty. The export buttons support routine documentation. CSV is useful for spreadsheets. PDF is useful for shared reports. Keep source values with every result. Clear records make later review easier. They also reduce transcription mistakes during class, field, or laboratory work and simple audit checks later.
FAQs
What is half life?
Half life is the time needed for half of a sample to decay, disappear, or transform under a first order model.
What does exponential decay mean?
Exponential decay means the sample loses a constant fraction over equal time intervals, not a constant amount.
Can I use grams instead of moles?
Yes. You can use grams, moles, atoms, activity, or any unit. Keep the same amount unit throughout the calculation.
Can this calculator find elapsed time?
Yes. Enter the initial amount, remaining amount, and either half life or decay constant. The calculator solves for time.
What is the decay constant?
The decay constant shows the fractional decay rate per time unit. It equals ln(2) divided by the half life.
Is mean lifetime the same as half life?
No. Mean lifetime equals one divided by the decay constant. Half life equals ln(2) divided by the decay constant.
Why must units match?
The equation needs consistent time units. If half life is in hours, elapsed time and decay constant must also use hours.
Does this work for all reactions?
No. It works for first order decay behavior. Do not use it for zero order or complex reaction systems without checking assumptions.