Activity from Number of Atoms Calculator

Calculator Input

Use the responsive grid below. Large screens show three columns, smaller screens show two, and mobile shows one.

Sample Name

Number of Atoms (N₀)

Known Radioactive Property

Half Life Value

Half Life Unit

Decay Constant Value

Decay Constant Unit

Elapsed Time

Elapsed Time Unit

Branching Ratio (%)

Detector Efficiency (%)

Example Data Table

These example values are illustrative and help verify the calculator workflow.

Sample	Initial Atoms	Half Life	Elapsed Time	Approx. Current Activity
Example A	1.00 × 10¹²	1 hour	0.5 hour	1.36 × 10⁸ Bq
Example B	5.00 × 10⁹	2 days	4 days	5.01 × 10³ Bq
Example C	3.20 × 10¹⁵	Using λ = 2.0 × 10^-7 s^-1	30 days	3.81 × 10⁸ Bq

Formula Used

1) Activity from atoms
A = λN
Activity equals decay constant multiplied by the number of undecayed atoms.

2) Decay constant from half life
λ = ln(2) / T_1/2
This converts half life into the decay constant used by the activity equation.

3) Remaining atoms after elapsed time
N(t) = N₀e^-λt
The atom count shrinks exponentially as time increases.

4) Branch adjusted activity
A_branch = A(t) × branching fraction
This is useful when only one decay branch is relevant.

5) Expected detected count rate
Count Rate = A_branch × detector efficiency
This estimates the observed rate when your detector does not capture every decay.

How to Use This Calculator

Enter a sample name if you want a labeled report.
Type the initial number of atoms in standard or scientific notation.
Select whether you know half life or decay constant.
Fill the matching decay input and choose its unit.
Enter elapsed time and its unit to find present activity.
Add branching ratio and detector efficiency when needed.
Press Calculate Activity to show results above the form.
Use the CSV or PDF buttons to export the calculated report.

Frequently Asked Questions

1) What does activity mean in radioactive decay?

Activity is the number of nuclear decays happening each second. Its SI unit is the becquerel, where 1 Bq equals 1 decay per second.

2) Why can activity be calculated from atom count?

Each atom has a probability of decaying per unit time. Multiplying that probability, represented by λ, by the number of atoms gives the expected decay rate.

3) Should I enter half life or decay constant?

Use whichever value you already know. The calculator converts half life to decay constant automatically, so both input methods lead to the same activity result.

4) Why does activity decrease after elapsed time?

As atoms decay, fewer unstable nuclei remain. Because activity depends on the remaining atoms, the decay rate drops exponentially with time.

5) What is branching ratio in this calculator?

Branching ratio is the percentage of decays that follow a specific decay path. It helps when you care about one emission or one measurable branch only.

6) What does detector efficiency change?

Detector efficiency estimates how many decays your instrument actually records. A lower efficiency means the observed count rate will be below the true branch activity.

7) Why does the graph go beyond my entered time?

The graph extends farther so you can see the broader decay trend. This makes comparison easier and shows how quickly activity falls across several half lives.

8) Can this calculator show activity in curies too?

Yes. The result table includes becquerels, curies, millicuries, and microcuries so you can compare common activity units easily.