Radiation Activity Decay Calculator

Radioactive Decay Law:

\[ A = A_0 e^{-\lambda t} \]

Current Activity (A):

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1. What is the Radioactive Decay Law?

The radioactive decay law describes how the activity of a radioactive substance decreases over time. It follows an exponential decay pattern where the rate of decay is proportional to the amount of radioactive material present.

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

\[ A = A_0 e^{-\lambda t} \]

Where:

\( A \) — Current activity (Bq)
\( A_0 \) — Initial activity (Bq)
\( \lambda \) — Decay constant (s⁻¹)
\( t \) — Time elapsed (s)
\( e \) — Euler's number (approximately 2.71828)

Explanation: The equation shows that radioactive decay follows an exponential pattern, with the decay constant determining how quickly the activity decreases over time.

3. Importance of Activity Calculation

Details: Accurate activity calculation is crucial for radiation safety, medical applications, archaeological dating, nuclear power operations, and scientific research involving radioactive materials.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between decay constant and half-life?
A: The decay constant (λ) and half-life (T½) are related by: λ = ln(2)/T½, where T½ is the time for activity to reduce to half its initial value.

Q2: What are common units for radioactive activity?
A: Becquerel (Bq) is the SI unit (1 decay per second). Curie (Ci) is another common unit where 1 Ci = 3.7×10¹⁰ Bq.

Q3: How accurate is the exponential decay model?
A: The exponential model is highly accurate for large numbers of atoms and is fundamental to radioactive decay physics.

Q4: Can this calculator be used for any radioactive isotope?
A: Yes, as long as you know the decay constant for that specific isotope and use consistent time units.

Q5: What if I know half-life instead of decay constant?
A: Convert half-life to decay constant using: λ = ln(2) / T½, where T½ is the half-life in seconds.