1. What is Half-life?

Half-life (t_1/2) 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 processes.

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 half-life is inversely proportional to the decay constant - the faster the decay, the shorter the half-life.

3. Importance of Half-life Calculation

Details: Half-life is crucial in radiometric dating, nuclear medicine, drug metabolism studies, and determining safe radiation exposure levels.

4. Using the Calculator

Tips: Enter the decay constant in reciprocal seconds (1/s). The value must be positive. The result will be in seconds.

5. Frequently Asked Questions (FAQ)

Q1: What's the relationship between half-life and decay constant?
A: They are inversely related. A larger decay constant means a shorter half-life, indicating faster decay.

Q2: Can I calculate decay constant from half-life?
A: Yes, rearrange the formula: λ = ln(2)/t_1/2

Q3: What are typical half-life values?
A: They vary widely - from fractions of a second for some isotopes to billions of years for others like Uranium-238.

Q4: How does half-life relate to radioactivity?
A: After each half-life, the radioactivity of a sample decreases by half.

Q5: Is half-life constant for a given substance?
A: Yes, it's a fundamental property of each radioactive isotope or decaying substance.