1. What is Decay Constant?

The decay constant (λ) represents the probability per unit time that a given nucleus will decay. It's a fundamental parameter in radioactive decay calculations, related to the half-life of a radioactive substance.

2. How Does the Calculator Work?

The calculator uses the decay constant formula:

Where:

• \( \lambda \) — Decay constant (s⁻¹)
• \( t_{1/2} \) — Half-life of the substance (seconds)
• \( \ln(2) \) — Natural logarithm of 2 (~0.693)

Explanation: The decay constant is inversely proportional to the half-life. A shorter half-life means a larger decay constant, indicating faster decay.

3. Importance of Decay Constant

Details: The decay constant is essential for calculating activity of radioactive samples, determining decay rates, and predicting how much radioactive material will remain after a given time.

4. Using the Calculator

Tips: Enter the half-life in seconds (convert from years if necessary). The value must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for decay constants?
A: Values vary widely - from ~10⁻²³ s⁻¹ for nearly stable nuclides to ~10¹⁸ s⁻¹ for extremely short-lived particles.

Q2: How does decay constant relate to activity?
A: Activity (A) = λN, where N is the number of radioactive nuclei. Higher λ means higher activity for a given N.

Q3: Can this be used for carbon dating?
A: Yes, ¹⁴C has a half-life of 5730 years, corresponding to λ ≈ 3.83 × 10⁻¹² s⁻¹.

Q4: What's the difference between λ and half-life?
A: They describe the same phenomenon but λ is used in differential equations while half-life is more intuitive.

Q5: How to convert between different time units?
A: First convert half-life to seconds, then calculate λ in s⁻¹. You can convert the result to other time units if needed.