1. What is Mean Life Time?

Mean Life Time is the average lifetime of an atomic nucleus in a radioactive sample. It represents the expected time until a radioactive atom decays.

2. How Does the Calculator Work?

The calculator uses the Mean Life Time formula:

Where:

• \( \zeta \) — Mean Life Time (in seconds)
• \( T_{1/2} \) — Radioactive Half Life (in seconds)

Explanation: The formula calculates the average lifetime of radioactive nuclei based on their half-life, with 1.446 being the conversion factor from half-life to mean life time.

3. Importance of Mean Life Time Calculation

Details: Calculating mean life time is crucial in nuclear physics for understanding radioactive decay processes, radiation safety calculations, and determining the stability of radioactive isotopes.

4. Using the Calculator

Tips: Enter the radioactive half-life in seconds. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between half-life and mean life time?
A: Mean life time is approximately 1.446 times the half-life of a radioactive substance.

Q2: Why is mean life time longer than half-life?
A: Mean life time represents the average lifetime of all atoms, while half-life is the time for half of the atoms to decay. Some atoms survive much longer than the half-life.

Q3: Can this formula be used for all radioactive elements?
A: Yes, this formula applies to all radioactive elements that follow exponential decay patterns.

Q4: What are the units for mean life time?
A: Mean life time is typically measured in seconds, but can be converted to other time units as needed.

Q5: How accurate is the 1.446 conversion factor?
A: The factor 1.446 is derived from the natural logarithm of 2 (ln(2) ≈ 0.693), where mean life time = half-life / ln(2) ≈ half-life × 1.4427. The value 1.446 provides a practical approximation.