1. What is the Isotope Decay Equation?

The isotope decay equation describes the fraction of radioactive material remaining after a given time period, based on its half-life. It follows the principle of exponential decay that is fundamental to nuclear physics and radiometric dating.

2. How Does the Calculator Work?

The calculator uses the decay equation:

Where:

• \( t \) — Elapsed time (same units as half-life)
• \( T \) — Half-life of the isotope (time for half the atoms to decay)

Explanation: The equation shows that the remaining fraction decreases exponentially with time, with the rate determined by the half-life.

3. Importance of Decay Calculation

Details: Calculating radioactive decay is essential for radiometric dating, nuclear medicine, radiation safety, and understanding nuclear processes in physics and geology.

4. Using the Calculator

Tips: Enter the elapsed time and half-life in consistent units (both in years, days, etc.). The calculator will show the remaining fraction and percentage of the original material.

5. Frequently Asked Questions (FAQ)

Q1: What is half-life?
A: Half-life is the time required for half of the radioactive atoms present to decay. It's a constant for each radioactive isotope.

Q2: Can I use different time units?
A: Yes, as long as both time and half-life use the same units (years, days, seconds, etc.).

Q3: What does the remaining fraction represent?
A: It's the portion of the original radioactive material that hasn't decayed after the given time.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for large numbers of atoms, following statistical decay laws.

Q5: Can this be used for carbon dating?
A: Yes, for carbon-14 which has a half-life of about 5730 years. The calculator can determine what fraction remains after a given time.