Radioactive Decay Calculation

Radioactive Decay Equation:

\[ \text{decay} = A_0 - A = A_0 (1 - e^{-\lambda t}) \]

Initial Activity (A₀):

Current Activity (A):

Decay Constant (λ):

1/time

Time (t):

time

Decay:

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1. What is Radioactive Decay?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. The decay equation calculates the amount of radioactive material that has decayed over a given time period.

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

\[ \text{decay} = A_0 - A = A_0 (1 - e^{-\lambda t}) \]

Where:

\( A_0 \) — Initial activity (Bq)
\( A \) — Current activity (Bq)
\( \lambda \) — Decay constant (1/time)
\( t \) — Time elapsed

Explanation: The equation calculates the amount of radioactive material that has decayed based on the initial activity, decay constant, and time elapsed.

3. Importance of Decay Calculation

Details: Calculating radioactive decay is essential for nuclear medicine, radiometric dating, radiation safety, and understanding nuclear processes.

4. Using the Calculator

Tips: Enter initial activity in becquerels (Bq), current activity in Bq, decay constant in reciprocal time units, and time in consistent units. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between activity and decay?
A: Activity measures current emissions, while decay quantifies how much has been lost over time.

Q2: How is the decay constant related to half-life?
A: The decay constant (λ) relates to half-life (t½) by λ = ln(2)/t½.

Q3: What units should I use for time?
A: Time units must match the decay constant units (e.g., if λ is in 1/years, time should be in years).

Q4: Can this calculate remaining activity?
A: Yes, remaining activity A = A₀ - decay = A₀e^(-λt).

Q5: What if I only know half-life?
A: First convert half-life to decay constant using λ = ln(2)/half-life.