1. What is Half-life?

Half-life (t_1/2) is the time required for a quantity to reduce to half its initial value. In chemistry, it describes how quickly unstable atoms undergo radioactive decay or how long stable atoms survive.

2. The Half-life Formula

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 (~0.693)

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 nuclear chemistry, radiometric dating, medical imaging, and determining proper dosages for radioactive pharmaceuticals.

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. A substance with high decay constant will have a short half-life, and vice versa.

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

Q3: How is half-life different from mean lifetime?
A: Mean lifetime (τ) is the average time before decay, related to half-life by τ = t_1/2/ln(2) ≈ 1.443 × t_1/2.

Q4: What are typical half-life values?
A: They range from fractions of a second for very unstable isotopes to billions of years for nearly stable ones.

Q5: How does temperature affect half-life?
A: For nuclear decay, half-life is essentially constant. For chemical reactions, it typically decreases with increasing temperature.