1. What is Half-life in Physics?

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

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 (~0.693147)

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 for determining the stability of radioactive isotopes, calculating safe radiation doses, dating archaeological finds (radiocarbon dating), and designing nuclear medicine treatments.

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 in seconds.

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. A higher decay constant means shorter half-life.

Q2: Can this calculator be used for any radioactive element?
A: Yes, as long as you know the decay constant, you can calculate the half-life for any isotope.

Q3: What are typical half-life values?
A: Half-lives range from fractions of a second (e.g., Polonium-214: 0.000164 seconds) to billions of years (e.g., Uranium-238: 4.468 billion years).

Q4: How accurate is this calculation?
A: The calculation is mathematically exact. Accuracy depends on how precisely you know the decay constant.

Q5: Can I calculate decay constant from half-life?
A: Yes, simply rearrange the formula: λ = ln(2)/t_1/2.