If the original activity of an Iridium source is 60 Ci, what will its activity be after 150 days?

To determine the activity of an Iridium source after a certain period, it is essential to understand the concept of radioactive decay and the half-life of the isotope in question. Iridium-192, which is commonly used in industrial radiography, has a half-life of approximately 74 days.

The decay of a radioactive isotope can be expressed using the formula:

[ A = A_0 \left( \frac{1}{2} \right)^{\frac{t}{t_{1/2}}} ]

where:

• ( A ) is the remaining activity,
• ( A_0 ) is the original activity,
• ( t ) is the elapsed time,
• ( t_{1/2} ) is the half-life.

In this case, the original activity ( A_0 ) is 60 Ci, and the elapsed time ( t ) is 150 days. To find out how many half-lives have occurred in 150 days, we calculate:

[ \frac{t}{t_{1/2}} = \frac{150 \text{ days}}{74 \text{ days}} \approx 2.02. ]

This indicates that a little over 2