1. What is the Decay Constant?

The decay constant (λ) represents the probability per unit time that a given radioactive atom will decay. It relates to the half-life (T_1/2) through a simple logarithmic relationship.

2. How Does the Calculator Work?

The calculator uses the decay constant equation:

Where:

• \( \lambda \) — Decay constant (per time unit)
• \( T_{1/2} \) — Half-life (same time unit)
• \( \ln(2) \) — Natural logarithm of 2 (~0.6931)

Explanation: The equation shows that the decay constant is inversely proportional to the half-life. A shorter half-life means a larger decay constant (faster decay).

3. Importance of Decay Constant

Details: The decay constant is fundamental in radioactive decay calculations, used to determine activity, remaining quantity, and decay rates in nuclear physics, radiometric dating, and medical applications.

4. Using the Calculator

Tips: Enter the half-life in any time unit (seconds, years, etc.). The result will be in reciprocal time units (per second, per year, etc.). Half-life must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between half-life and decay constant?
A: They are inversely related through the natural logarithm of 2. Shorter half-life means larger decay constant.

Q2: What are typical units for decay constant?
A: Common units include s^-1, min^-1, yr^-1, matching the half-life units used.

Q3: Can this be used for any radioactive isotope?
A: Yes, as long as you know the half-life, this equation applies to all exponential decay processes.

Q4: Why is ln(2) used in the equation?
A: It comes from solving the differential equation for decay when the quantity reaches half its original value.

Q5: How is this different from mean lifetime?
A: Mean lifetime (τ) is 1/λ, while half-life is ln(2)/λ. Mean lifetime is about 44% longer than half-life.