If the half-life of tritium is 12.3 years, what percentage of a sample would remain after 123 years?

To determine what percentage of a tritium sample would remain after 123 years, knowing the half-life of tritium is 12.3 years, we can use the concept of half-lives.

First, we need to find out how many half-lives fit into the 123 years. This is done by dividing the total time by the half-life:

[ \text{Number of half-lives} = \frac{123 \text{ years}}{12.3 \text{ years/half-life}} \approx 10 \text{ half-lives} ]

Next, we can calculate the remaining amount of tritium using the formula that describes exponential decay based on the number of half-lives:

[ \text{Remaining Percentage} = \left( \frac{1}{2} \right)^{n} \times 100 ]

where ( n ) is the number of half-lives. So, after 10 half-lives, the calculation becomes:

[ \text{Remaining Percentage} = \left( \frac{1}{2} \right)^{10} \times 100 ]

Calculating ( \left( \frac{1}{