Radiation Decay Calculator

Radiation Decay Formula:

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

Current Activity (A):

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1. What is Radiation Decay?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. The decay follows an exponential law described by the fundamental decay equation.

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

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

Where:

\( A \) — Current activity (Bq)
\( A_0 \) — Initial activity (Bq)
\( \lambda \) — Decay constant (s⁻¹)
\( t \) — Time elapsed (seconds)
\( e \) — Base of natural logarithm (~2.71828)

Explanation: The equation shows how activity decreases exponentially over time, with the rate of decrease determined by the decay constant.

3. Importance of Radiation Decay Calculation

Details: Calculating radioactive decay is essential for radiation safety, nuclear medicine, radiometric dating, and understanding the behavior of radioactive materials over time.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between decay constant and half-life?
A: The half-life (t₁/₂) is related to the decay constant by: t₁/₂ = ln(2)/λ ≈ 0.693/λ.

Q2: What units should I use for the decay constant?
A: The decay constant must be in reciprocal seconds (s⁻¹) to match the time units. If you have half-life instead, first convert it to decay constant.

Q3: Can this calculator be used for any radioactive isotope?
A: Yes, as long as you know the decay constant (or can calculate it from half-life), this equation applies to all radioactive decay processes.

Q4: Why does the activity decrease exponentially?
A: The probability of decay per unit time is constant for each radioactive atom, leading to an exponential decrease in the number of remaining atoms over time.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal radioactive decay. In practice, other factors like measurement precision and sample purity affect real-world accuracy.