1. What is the Decay Constant?

The decay constant (λ) is a probability rate that describes how quickly unstable atomic nuclei undergo radioactive decay. It's inversely related to the half-life of a radioactive substance.

2. How Does the Calculator Work?

The calculator uses the decay constant equation:

Where:

• \( \lambda \) — Decay constant (1/s)
• \( t_{1/2} \) — Half-life of the radioactive substance (seconds)
• \( \ln(2) \) — Natural logarithm of 2 (~0.6931)

Explanation: The equation shows that substances with shorter half-lives have larger decay constants, meaning they decay more rapidly.

3. Importance of Decay Constant

Details: The decay constant is fundamental in nuclear physics for calculating activity, predicting decay rates, and determining radiation safety measures.

4. Using the Calculator

Tips: Enter the half-life in seconds (convert from other units if necessary). The result will be the decay constant in reciprocal seconds (1/s).

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 and faster decay.

Q2: Can I use other time units besides seconds?
A: Yes, but you must convert to seconds first. The result will always be in 1/s.

Q3: What does the decay constant physically represent?
A: It represents the probability per unit time that any given nucleus will decay.

Q4: How is this used in radioactive dating?
A: By measuring remaining radioactive material and knowing λ, we can calculate age using \( t = \frac{1}{\lambda} \ln(\frac{N_0}{N}) \).

Q5: What's the difference between decay constant and activity?
A: Activity (A) is the product of decay constant (λ) and number of nuclei (N): A = λN.