1. What is Radioactive Decay Half-life?

The half-life of a radioactive isotope is the time required for half of the radioactive atoms present to decay. It's a fundamental property of each radioactive isotope.

2. How Does the Calculator Work?

The calculator uses the decay equation:

Where:

• \( t \) — Half-life (time)
• \( \lambda \) — Decay constant (1/time)
• \( \ln(2) \) — Natural logarithm of 2 (~0.693)

Explanation: The equation shows the inverse relationship between decay constant and half-life - isotopes with larger decay constants decay faster.

3. Importance of Half-life Calculation

Details: Knowing half-life is essential for radiometric dating, medical applications of radioisotopes, nuclear power generation, and radioactive waste management.

4. Using the Calculator

Tips: Enter the decay constant in reciprocal time units (1/s, 1/year, etc.). The result will be in the same time units as used for the decay constant.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between half-life and decay constant?
A: Both describe decay rate but half-life is more intuitive (time for half to decay) while decay constant is the probability per unit time that an atom will decay.

Q2: Can this calculator work for any radioactive isotope?
A: Yes, as long as you know the decay constant, the equation applies universally to all radioactive decay processes.

Q3: What are typical half-life values?
A: They 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 precise is this calculation?
A: The calculation is mathematically exact - precision depends on how accurately you know the decay constant.

Q5: Can I calculate decay constant from half-life?
A: Yes, just rearrange the equation: λ = ln(2)/t_1/2