1. What is Radioactive Decay?

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

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

Where:

• \( A \) — Activity at time t (Becquerel)
• \( A_0 \) — Initial activity (Becquerel)
• \( \lambda \) — Decay constant (s⁻¹)
• \( t \) — Time elapsed (seconds)
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The equation describes how the activity of a radioactive substance decreases exponentially over time, with the rate of decay determined by the decay constant.

3. Importance of Radioactive Decay Calculation

Details: Accurate calculation of radioactive decay is crucial for nuclear medicine, radiation safety, radiometric 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 (T₁/₂) are related by: \( T_{1/2} = \frac{\ln(2)}{\lambda} \)

Q2: What is a Becquerel (Bq)?
A: One Becquerel represents one radioactive decay per second. It is the SI unit of radioactivity.

Q3: Can this calculator be used for any radioactive isotope?
A: Yes, as long as you know the decay constant for that specific isotope.

Q4: What if I have multiple radioactive isotopes?
A: For multiple isotopes, calculate each decay separately and sum the activities, unless they are in a decay chain.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for a single radioactive isotope undergoing exponential decay.