1. What is a Radionuclide Decay Calculator?

Definition: This calculator determines the remaining activity of a radioactive substance after a given time period using the exponential decay law.

Purpose: It helps nuclear scientists, medical professionals, and researchers predict radioactive material behavior over time.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Current activity (Becquerel)
• \( A_0 \) — Initial activity (Becquerel)
• \( \lambda \) — Decay constant (per second)
• \( t \) — Elapsed time (seconds)
• \( e \) — Euler's number (~2.71828)

Explanation: The initial activity decreases exponentially over time based on the substance's decay constant.

3. Importance of Decay Calculation

Details: Accurate decay calculations are essential for radiation safety, medical treatments, radiometric dating, and nuclear waste management.

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 (time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: How is decay constant related to half-life?
A: Decay constant (λ) = ln(2)/half-life. They are inversely proportional.

Q2: What's a typical decay constant value?
A: Values vary widely. For example, Iodine-131 has λ≈9.98×10⁻⁷ s⁻¹ while Carbon-14 has λ≈3.83×10⁻¹² s⁻¹.

Q3: Can I use different time units?
A: Yes, but ensure your decay constant uses matching reciprocal time units (min⁻¹ for minutes, yr⁻¹ for years, etc.).

Q4: What if I know half-life instead of decay constant?
A: First calculate λ = ln(2)/half-life, then use that value in the calculator.

Q5: Why does the result have many decimal places?
A: Radioactive decay calculations often require high precision, especially for small decay constants or short time periods.