1. What is a Radioactive Decay Calculator?

Definition: This calculator determines the current activity of a radioactive substance based on its initial activity, decay constant, and elapsed time.

Purpose: It helps physicists, engineers, and medical professionals understand radioactive decay processes and predict material activity over time.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• \( A \) — Current activity (Becquerel)
• \( A_0 \) — Initial activity (Becquerel)
• \( \lambda \) — Decay constant (per second)
• \( t \) — Elapsed time (seconds)

Explanation: The formula describes how the activity of a radioactive substance decreases exponentially over time.

3. Importance of Radioactive Decay Calculation

Details: Accurate decay calculations are crucial for radiation safety, medical treatments, nuclear power, and radiometric dating.

4. Using the Calculator

Tips: Enter the initial activity in Bq, decay constant in s⁻¹, and time in seconds. All values must be positive (except time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between decay constant and half-life?
A: Half-life (t½) = ln(2)/λ. The decay constant and half-life are inversely proportional.

Q2: What units are used for activity?
A: The SI unit is Becquerel (Bq), where 1 Bq = 1 decay per second. The traditional unit is Curie (1 Ci = 3.7×10¹⁰ Bq).

Q3: Can I use this for any radioactive isotope?
A: Yes, as long as you know the decay constant (or can calculate it from the half-life).

Q4: How do I find the decay constant for a specific isotope?
A: Look up the half-life in reference tables and calculate λ = ln(2)/t½.

Q5: Why does the formula use exponential decay?
A: Radioactive decay is a random process where the decay probability per nucleus is constant, leading to exponential decrease.