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 and physics, it's commonly used to describe the rate of radioactive decay or the elimination of substances from biological systems.

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 in radiometric dating, nuclear medicine, pharmacokinetics, and environmental science to understand how quickly substances decay or are eliminated from systems.

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 - as decay constant increases, half-life decreases, indicating faster decay.

Q2: Can this calculator be used for biological half-life?
A: Yes, the same formula applies to biological elimination half-life when you know the elimination rate constant.

Q3: What are typical units for half-life?
A: While we use seconds here, half-life can be expressed in any time unit (minutes, hours, years) as long as the decay constant uses reciprocal units.

Q4: How is half-life related to mean lifetime?
A: Mean lifetime (τ) is related to half-life by: τ = t_1/2/ln(2) ≈ 1.4427 × t_1/2.

Q5: What if I know half-life and want to find decay constant?
A: Simply rearrange the formula: λ = ln(2)/t_1/2.