An element has a half-life of 24 hours. What fraction of the atoms has disintegrated in 72 hours?

The half-life of the element ($T_{1/2}$) is 24 hours.
The total time ($t$) is 72 hours.

The number of half-lives is given by the formula:

Substitute the given values:

So, 3 half-lives have passed.

After $n$ half-lives, the fraction of the substance remaining is given by:

Substitute the value of $n$:

The fraction disintegrated is the total initial amount (which is 1) minus the fraction remaining:

The fraction of the atoms that has disintegrated in 72 hours is $\frac{7}{8}$.

The final answer is $\text{A. } \frac{7}{8}$.