1. What is the Decay Constant?

The decay constant (λ) represents the probability per unit time that a given nucleus will decay. It relates to the half-life (T_1/2) through the natural logarithm of 2 (≈0.693).

2. How Does the Calculator Work?

The calculator uses the decay constant equation:

Where:

• \( \lambda \) — Decay constant (time^-1)
• \( T_{1/2} \) — Half-life (time units)
• \( \ln(2) \) — Natural logarithm of 2 (~0.693147)

Explanation: The equation shows that materials with shorter half-lives have larger decay constants (faster decay rates).

3. Importance of Decay Constant

Details: The decay constant is fundamental in nuclear physics, radiometric dating, medical imaging, and radiation therapy. It helps predict radioactive decay rates and material stability.

4. Using the Calculator

Tips: Enter the half-life in any time unit (seconds, years, etc.). The calculator will return the decay constant in reciprocal time units.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between half-life and decay constant?
A: They are inversely related - shorter half-life means larger decay constant (faster decay).

Q2: Can I use different time units?
A: Yes, but your decay constant units will match (e.g., years input gives years^-1 output).

Q3: Why is ln(2) used in the formula?
A: It comes from solving the differential equation for exponential decay when half the material remains.

Q4: What's the mean lifetime (τ) relation?
A: Mean lifetime τ = 1/λ = T_1/2/ln(2) ≈ 1.443 × T_1/2.

Q5: Does this work for all radioactive elements?
A: Yes, for any material following exponential decay, regardless of half-life duration.