1. What is Radioactive Decay Time?

The radioactive decay time equation calculates the time required for a radioactive substance to decay from its initial activity to its current activity, based on the decay constant.

2. How Does the Calculator Work?

The calculator uses the decay time equation:

Where:

• \( t \) — Decay time (same units as 1/λ)
• \( A_0 \) — Initial activity (Bq)
• \( A \) — Current activity (Bq)
• \( \lambda \) — Decay constant (1/time)

Explanation: The equation calculates the time required for radioactive decay based on the natural logarithm of the activity ratio divided by the decay constant.

3. Importance of Decay Time Calculation

Details: Calculating decay time is crucial for radiometric dating, nuclear medicine treatments, radioactive waste management, and understanding nuclear processes.

4. Using the Calculator

Tips: Enter initial and current activity in becquerels (Bq), and decay constant in reciprocal time units (1/s, 1/min, etc.). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the decay constant?
A: The decay constant units (1/time) should match your desired time units for the result (e.g., use 1/s to get time in seconds).

Q2: How is this related to half-life?
A: Half-life (t₁/₂) is related to the decay constant by t₁/₂ = ln(2)/λ. You can convert between them if needed.

Q3: Can I use this for any radioactive isotope?
A: Yes, as long as you know the correct decay constant for that isotope.

Q4: What if my current activity is higher than initial?
A: This would give a negative time, which is physically impossible. Current activity must be less than initial activity.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for simple radioactive decay. Accuracy depends on your input values.