How old id an artifact if only 1/4 of the hydrogen 3 in the sample remains?
To determine the age of an artifact based on the remaining quantity of Hydrogen-3, also known as Tritium, we can utilize its half-life.
The half-life of Tritium is approximately 12.32 years. This means that every 12.32 years, the quantity of Tritium reduces by half. Therefore, if only 1/4 of the original Tritium remains, we can work backward to calculate the age.
Let's assume the initial quantity of Tritium in the artifact was 100 units. If only 1/4 of the Tritium remains, we currently have 1/4 * 100 = 25 units left.
Next, we need to determine how many half-lives it took for the quantity to reduce from 100 to 25 units.
To calculate this, we can use the formula:
Number of half-lives = log(base 2) (Initial amount / Remaining amount)
Number of half-lives = log(base 2) (100/25)
In this case, log(base 2) (4) = 2
Therefore, it took 2 half-lives for the quantity of Tritium to reduce from 100 to 25 units.
Since the half-life of Tritium is approximately 12.32 years, we can multiply 2 half-lives by this time period to determine the age of the artifact.
Age of the artifact = 2 * 12.32 years = 24.64 years
Therefore, if only 1/4 of the Tritium remains in the sample, the artifact is approximately 24.64 years old.