Calculating the Remaining Amount of Actinium-228

Understanding the Calculation:

The half-life of actinium-228: The half-life of actinium-228 is 6.13 hours, which means that half of the initial amount of actinium-228 will decay in that time period. This information is crucial in determining the remaining amount of actinium-228 after a certain duration.

Using the Half-Life Formula:

To calculate the amount of actinium-228 remaining after 24.52 hours, we can utilize the half-life formula:

Amount remaining = Initial amount × (1/2)^(t / half-life)

Applying the Values:

Given that we have a 70 milligram sample of actinium-228 and a half-life of 6.13 hours, we substitute these values into the formula:

Amount remaining = 70 mg × (1/2)^(24.52 / 6.13)

Solving for the Remaining Amount:

By solving the equation, we determine that approximately 5.22 milligrams of actinium-228 will remain after 24.52 hours.

In conclusion, understanding the concept of half-life and applying the appropriate formula allows us to calculate the remaining amount of actinium-228 accurately. In this scenario, we found that only about 5.22 milligrams of actinium-228 will be left from the original 70 milligram sample after 24.52 hours.