Answer:
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.