What is the mean life of a 192 Ir source calculated using its half-life?

What is the mean life of a 192 Ir source calculated using its half-life?

• A. 106.5 days
• B. 30 years
• C. 1626 years
• D. 59.6 days

Answer: (A)

The mean life of a radioactive source is a calculation that represents the average time a nucleus remains in an unstable state before it decays. For any given radioactive isotope, the mean life can be derived from its half-life using the relationship that connects the mean life (τ) and the half-life (t₁/₂) through the formula τ = t₁/₂ / ln(2), where ln(2) is the natural logarithm of 2, approximately equal to 0.693. For a 192 Ir source, the half-life is about 73.83 days. Applying the formula: τ = 73.83 days / 0.693 ≈ 106.5 days. This calculation accurately yields the mean life as approximately 106.5 days, which corresponds to the correct answer choice. The mean life provides valuable context for understanding how long, on average, the isotope will exist before decaying, which is crucial in applications like radiation therapy where timing can be critical for treatment planning.

The mean life of a radioactive source is a calculation that represents the average time a nucleus remains in an unstable state before it decays. For any given radioactive isotope, the mean life can be derived from its half-life using the relationship that connects the mean life (τ) and the half-life (t₁/₂) through the formula τ = t₁/₂ / ln(2), where ln(2) is the natural logarithm of 2, approximately equal to 0.693.

For a 192 Ir source, the half-life is about 73.83 days. Applying the formula:

τ = 73.83 days / 0.693 ≈ 106.5 days.

This calculation accurately yields the mean life as approximately 106.5 days, which corresponds to the correct answer choice. The mean life provides valuable context for understanding how long, on average, the isotope will exist before decaying, which is crucial in applications like radiation therapy where timing can be critical for treatment planning.