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 equation N = N₀e^(-λt), where N is the remaining quantity, N₀ is the initial quantity, λ is the decay constant, and t is time.

2. How Does the Calculator Work?

The calculator uses the radioactive decay equation:

Where:

• \( N \) — Remaining quantity (atoms)
• \( N_0 \) — Initial quantity (atoms)
• \( \lambda \) — Decay constant (1/time)
• \( t \) — Elapsed time

Explanation: The equation shows how the quantity of radioactive material decreases exponentially over time.

3. Importance of Decay Calculation

Details: Calculating radioactive decay is crucial for nuclear physics, radiometric dating, medical applications, and radiation safety.

4. Using the Calculator

Tips: Enter initial quantity in atoms, decay constant in 1/time units, and time in consistent units. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: What are typical units for decay constant?
A: Common units are 1/seconds (s⁻¹), but any reciprocal time unit can be used (hours⁻¹, years⁻¹, etc.).

Q3: Can this calculate half-life directly?
A: No, this calculates remaining quantity. For half-life, use t₁/₂ = ln(2)/λ.

Q4: Does this work for all radioactive materials?
A: Yes, the exponential decay law applies to all radioactive substances, though some have complex decay chains.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for simple decay processes with constant λ.