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 radioactive decay or other exponential decay processes. It's a fundamental concept in nuclear physics, chemistry, and pharmacokinetics.

2. How Does the Calculator Work?

The calculator uses the half-life formula:

Where:

• \( t_{1/2} \) — Half-life (time units)
• \( \lambda \) — Decay constant (1/time units)
• \( \ln(2) \) — Natural logarithm of 2 (~0.6931)

Explanation: The formula shows the inverse relationship between half-life and decay constant - the faster the decay (higher λ), the shorter the half-life.

3. Importance of Half-Life Calculation

Details: Half-life calculations are essential for determining:

• Radioactive material safety and storage requirements
• Dosage intervals for pharmaceuticals
• Carbon dating in archaeology
• Nuclear power plant operations

4. Using the Calculator

Tips:

• Enter the decay constant in reciprocal time units (e.g., 1/s, 1/day, 1/year)
• The decay constant must be greater than zero
• The result will be in the same time units as the reciprocal of your input

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between half-life and decay constant?
A: Half-life is the time for half decay, while decay constant (λ) is the probability of decay per unit time. They're inversely related.

Q2: How do I convert between different time units?
A: If you enter λ in 1/sec, the half-life will be in seconds. For days, multiply seconds by 86400 (60×60×24).

Q3: Can this be used for biological half-life?
A: Yes, the same formula applies to biological elimination processes that follow exponential decay.

Q4: What if I know half-life and want to find decay constant?
A: Rearrange the formula: λ = ln(2)/t_1/2

Q5: Why is ln(2) used in the formula?
A: It comes from solving the exponential decay equation for when the quantity reaches half its original value.