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 to describe how quickly unstable atoms undergo radioactive decay.

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 (~0.6931)

Explanation: The formula shows that 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 calculations are essential in nuclear physics, radiometric dating, medical imaging, radiation therapy, and understanding radioactive waste management.

4. Using the Calculator

Tips: Enter the decay constant in units of 1/seconds. The value must be positive (λ > 0). The calculator will output the 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. A larger decay constant means a shorter half-life, indicating faster decay.

Q2: Can this calculator be used for biological half-life?
A: Yes, the same formula applies to biological half-life of substances in organisms, though the decay constant would represent biological elimination rates.

Q3: What are typical half-life values in nuclear physics?
A: Half-lives range from fractions of a second (e.g., Polonium-214: 0.000164 seconds) to billions of years (e.g., Uranium-238: 4.5 billion years).

Q4: How is half-life related to activity?
A: Activity (decays per second) is directly proportional to the number of atoms and inversely proportional to the half-life.

Q5: Can you calculate remaining quantity using half-life?
A: Yes, remaining quantity = initial × (1/2)^(t/t_1/2), where t is elapsed time.