1. What is Half-Life?

Half-life is the time required for a quantity to reduce to half its initial value. It's commonly used in nuclear physics, chemistry, and pharmacokinetics to describe exponential decay.

2. How Does the Calculator Work?

The calculator uses the half-life formula:

Where:

• \( \lambda \) — Decay constant (rate of decay)
• \( \ln(2) \) — 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 thus shorter half-life.

3. Importance of Half-Life Calculation

Details: Half-life calculations are essential in radiometric dating, medical treatments using radioactive isotopes, determining drug dosages, and understanding chemical reaction kinetics.

4. Using the Calculator

Tips: Enter the decay constant (λ) in units of 1/time (e.g., 1/sec, 1/min, 1/year). The value must be greater than zero. The result will be in the same time units as your decay constant.

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)/λ, so as λ increases, half-life decreases.

Q2: Can half-life be calculated for any substance?
A: Only for substances that undergo exponential decay, such as radioactive isotopes or drugs eliminated by first-order kinetics.

Q3: What are typical units for half-life?
A: The units depend on the decay constant. If λ is in 1/sec, half-life will be in seconds; if λ is in 1/year, half-life will be in years.

Q4: How does half-life relate to mean lifetime?
A: Mean lifetime (τ) is 1/λ, while half-life is ln(2)/λ, so mean lifetime is longer than half-life by a factor of 1/ln(2) ≈ 1.4427.

Q5: Can this formula be used for biological half-life?
A: Yes, it applies to biological elimination processes that follow first-order kinetics, like drug clearance from the body.