1. What is Half-Life?

Half-life is the time required for a quantity to reduce to half its initial value. In radioactive decay, it's the time needed for half of the radioactive atoms in a sample to undergo radioactive decay.

2. How Does the Calculator Work?

The calculator uses the half-life equation:

Where:

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

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

3. Importance of Half-Life Calculation

Details: Half-life calculations are essential in nuclear physics, radiometric dating, medical imaging, radiation therapy, and understanding the stability of radioactive isotopes.

4. Using the Calculator

Tips: Enter the decay constant in s⁻¹. The value must be greater than zero. The result will be displayed in seconds.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between half-life and decay constant?
A: Half-life and decay constant are inversely proportional. t_1/2 = ln(2)/λ

Q2: Can half-life be calculated for non-radioactive processes?
A: Yes, the concept of half-life applies to any exponential decay process, including chemical reactions and pharmacokinetics.

Q3: How does half-life relate to radioactivity?
A: Shorter half-life means more radioactive decay per unit time, resulting in higher radioactivity.

Q4: What are typical half-life values?
A: Half-lives range from fractions of a second to billions of years, depending on the isotope.

Q5: How is half-life measured experimentally?
A: By measuring the decrease in radioactivity over time and fitting the data to an exponential decay curve.