1. What is Half-Life?

Half-life (t_1/2) is the time required for a quantity to reduce to half of its initial value in radioactive decay. It's a fundamental concept in nuclear physics and chemistry.

2. How Does the Calculator Work?

The calculator uses the half-life formula:

Where:

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

Explanation: The formula shows that half-life is inversely proportional to the decay constant. A larger decay constant means faster decay and shorter half-life.

3. Importance of Half-Life Calculation

Details: Half-life calculations are essential in radiometric dating, nuclear medicine, radiation safety, and understanding radioactive decay processes.

4. Using the Calculator

Tips: Enter the decay constant in reciprocal seconds (1/s). The value must be positive. The calculator will compute the corresponding half-life.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between half-life and decay constant?
A: They are inversely related. Half-life = ln(2)/decay constant. Higher decay constants mean shorter half-lives.

Q2: Can I calculate decay constant from half-life?
A: Yes, decay constant = ln(2)/half-life. This calculator can be used in reverse for that purpose.

Q3: What are typical half-life values?
A: They vary widely - from fractions of a second for very unstable isotopes to billions of years for nearly stable ones.

Q4: Why is ln(2) used in the formula?
A: It comes from solving the differential equation for exponential decay when the remaining quantity is half (1/2) the original.

Q5: Does half-life depend on initial amount?
A: No, half-life is constant for a given radioactive substance regardless of the initial quantity.