1. What is Radioactive 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 differential equation dN/dt = -λN, where N is the number of atoms, λ is the decay constant.

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

Where:

• \( \frac{dN}{dt} \) — Decay rate (atoms/time)
• \( \lambda \) — Decay constant (1/time)
• \( N \) — Number of remaining atoms

Solution: The equation integrates to \( N(t) = N_0 e^{-\lambda t} \), where \( N_0 \) is the initial number of atoms.

3. Importance of Decay Calculations

Details: These calculations are essential in nuclear physics, radiometric dating, medical imaging, and radiation safety. They help determine material half-lives and decay rates.

4. Using the Calculator

Tips: Enter the initial number of atoms, decay constant (λ), and time period. All values must be positive (time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between λ and half-life?
A: Half-life (t₁/₂) = ln(2)/λ. The decay constant λ determines how quickly a substance decays.

Q2: What units should I use for λ?
A: The time units for λ should match your time input (e.g., if λ is in 1/years, time should be in years).

Q3: Can this calculate activity in becquerels?
A: Yes, activity (A) = λN. 1 becquerel = 1 decay per second.

Q4: Does this work for all radioactive isotopes?
A: Yes, as long as you know the correct decay constant for the specific isotope.

Q5: What if I have multiple decay modes?
A: For multiple decay paths, use the total decay constant (sum of all individual decay constants).