How much time will elapse if a radioisotope with a half-life of 88 seconds decays to one-sixteenth of its original mass?

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.

Explanation:

The decay of radioisotopes are represented by the following ordinary differential equation:

Where:

- Time, measured in seconds.

- Time constant, measured in seconds.

- Mass of the radioisotope, measured in grams.

The solution of this expression is:

Where is the initial mass of the radioisotope, measured in kilograms.

The ratio of current mass to initial mass is:

The time constant is now calculated in terms of half-life:

Where is the half-life of the radioisotope, measured in seconds.

Given that , the time constant of the radioisotope is:

Now, if and , the time is:

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.