1. What is the Half-life Formula?

The half-life formula calculates the time required for a quantity to reduce to half its initial value in radioactive decay processes. It's a fundamental concept in nuclear physics and chemistry.

2. How Does the Calculator Work?

The calculator uses the half-life formula:

Where:

• \( T \) — Half-life (time)
• \( \lambda \) — Decay constant (1/time)
• \( \ln(2) \) — 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 a shorter half-life.

3. Importance of Half-life Calculation

Details: Half-life calculations are essential for determining the stability of radioactive isotopes, dating archaeological finds, medical applications of radioisotopes, and nuclear safety assessments.

4. Using the Calculator

Tips: Enter the decay constant in reciprocal time units (1/s, 1/day, etc.). The value must be positive. The calculator will output the half-life in the same time units.

5. Frequently Asked Questions (FAQ)

Q1: What are typical units for decay constant and half-life?
A: Common units include seconds (s⁻¹), minutes (min⁻¹), hours (hr⁻¹), days (day⁻¹), or years (yr⁻¹). The half-life will be in the reciprocal time unit.

Q2: How is half-life related to radioactive decay?
A: Half-life characterizes how quickly unstable atomic nuclei undergo radioactive decay. After each half-life, half of the remaining radioactive atoms decay.

Q3: Can this formula be used for non-radioactive processes?
A: Yes, the same mathematics applies to any first-order decay process, including chemical reactions and pharmacokinetics.

Q4: What's the difference between half-life and mean lifetime?
A: Mean lifetime (τ) is the average time before decay, related to half-life by τ = T / ln(2) ≈ 1.4427 × T.

Q5: How accurate is this calculation?
A: The formula is mathematically exact for first-order decay processes. Accuracy depends on precise measurement of the decay constant.