Example Data Table
| Question | Initial | Half Life | Time | Expected Result |
|---|---|---|---|---|
| Carbon-14 classroom sample | 100 g | 5730 years | 11460 years | 25 g remains |
| Iodine-131 medicine sample | 80 mg | 8.02 days | 16.04 days | 20 mg remains |
| Cobalt-60 lab source | 48 g | 5.2714 years | 10.5428 years | 12 g remains |
Formula Used
Remaining amount: N = N0 × (1 / 2)t / T
Initial amount: N0 = N ÷ (1 / 2)t / T
Elapsed time: t = T × log2(N0 / N)
Half life: T = t ÷ log2(N0 / N)
Decay constant: λ = ln(2) ÷ T
Activity: A = λN, when N is atoms present.
How To Use This Calculator
- Select a preset isotope, or choose a custom sample.
- Pick the calculation type that matches your chemistry question.
- Enter the known amount, time, half life, or ratio values.
- Choose matching units for time and half-life fields.
- Use half lives directly when the worksheet gives them.
- Press Calculate to show the answer above the form.
- Use CSV or PDF buttons to save the worked result.
Half Life Calculation Guide
What Half Life Means
Half life describes how long a radioactive sample takes to lose half of its unchanged nuclei. It is a fixed property for a given isotope. It does not depend on the starting mass. A large sample and a small sample share the same half life.
Why The Ratio Matters
Many instructional chemistry problems give an initial amount and a final amount. The ratio between these values tells how many half lives passed. For example, one half life leaves one half. Two half lives leave one fourth. Three half lives leave one eighth.
Advanced Input Options
This calculator accepts mass, moles, atoms, activity units, elapsed time, decay constants, and direct half-life counts. It also supports preset isotopes used in common lessons. You can still enter a custom value when a worksheet gives a special isotope or rounded classroom number.
Using Time Units Correctly
Time units can cause wrong answers. A half life in days must be compared with a time in days. This tool converts seconds, minutes, hours, days, and years internally. The output unit can be changed for easier reporting.
Decay Constant Method
The decay constant is another way to describe radioactive change. It is written as lambda. A larger lambda means faster decay. The relation between half life and lambda is simple. Lambda equals natural log of two divided by half life.
Activity Calculations
Activity estimates the number of decays each second. It is calculated from atoms present and the decay constant per second. This feature is useful for advanced chemistry and nuclear science practice. It also helps connect half-life lessons with measurement ideas.
Checking Instructional Answers
Use the result table to compare each step with classroom answers. Review the number of half lives first. Then check the remaining fraction. Finally compare the final amount. This process makes errors easier to find before submitting work.
FAQs
What is half life in chemistry?
Half life is the time required for half of a radioactive sample to decay. It is constant for a given isotope under normal classroom assumptions.
Can this calculator find remaining mass?
Yes. Enter the initial amount, half life, and elapsed time. You may also enter the number of half lives directly.
Can I calculate the original amount?
Yes. Select initial amount. Then enter the remaining amount and either time with half life or the half-life count.
What does decay constant mean?
The decay constant shows the probability rate of decay. It equals ln(2) divided by the half life in the same time scale.
Why are my units important?
Half life and elapsed time must match logically. This tool converts common time units, but your input choices still need to match the question.
Can I use worksheet half-life counts?
Yes. Enter the number of half lives directly. The calculator can then find remaining percent or remaining amount without elapsed time.
Does mass affect half life?
No. The half life of an isotope is independent of sample size. More material has more atoms, but the same decay pattern.
What is activity in this tool?
Activity is the estimated decays per second. It uses the atom count and the decay constant per second.