1. What is the Decay Rate Equation?

The decay rate equation calculates the rate of radioactive decay based on the decay constant and the number of radioactive atoms present. It's fundamental in nuclear physics and radiometric dating.

2. How Does the Calculator Work?

The calculator uses the decay rate equation:

Where:

• \( \lambda \) — Decay constant (probability of decay per unit time)
• \( N \) — Number of radioactive atoms present

Explanation: The equation shows that the decay rate is directly proportional to both the decay constant and the number of radioactive atoms.

3. Importance of Decay Rate Calculation

Details: Calculating decay rate is essential for determining the activity of radioactive samples, understanding half-life, and applications in medicine, archaeology, and nuclear energy.

4. Using the Calculator

Tips: Enter the decay constant in units of 1/time (e.g., 1/s, 1/year) and the number of radioactive atoms. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between decay rate and half-life?
A: The decay constant (λ) is related to half-life (t½) by λ = ln(2)/t½. Half-life is more commonly used in practice.

Q2: What are typical units for decay rate?
A: Common units are becquerels (Bq, decays per second) or curies (Ci, 3.7×10¹⁰ decays per second).

Q3: Does decay rate change over time?
A: Yes, as the number of radioactive atoms decreases, the decay rate decreases proportionally.

Q4: Can this calculator be used for any radioactive isotope?
A: Yes, as long as you know the decay constant and current number of atoms, the equation applies universally.

Q5: How accurate is this calculation?
A: It's mathematically exact for a large number of atoms. For very small numbers of atoms, statistical fluctuations become significant.