A pure sample of tritium, ³H, was prepared and sealed in a container for a number of years. Tritium undergoes β decay with a half-life of 12.32 years. How long has the container been sealed if analysis of the contents shows there are 5.25 mol of ³H and 6.35 mol of ³He present?

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The fact that there is ³He present indicates that β decay of tritium has taken place. Specifically, one of the neutrons in tritium has decayed into a proton, releasing an electron (β particle) and a neutrino. This converts tritium into helium-3 (³He), while conserving both mass and charge. The balanced nuclear equation is: ³H -> ³He + e- + ν We don't know the initial amounts of tritium versus helium-3, but we do know the ratio of their current amounts. Since tritium has a half-life of 12.32 years, we can use the ratio of the current amounts to calculate how many half-lives have passed. Then we can use the half-life to determine the total time elapsed. Here's how: Let x = number of half-lives that have passed Then, according to the ratio of current amounts: 5.25 mol ³H / 6.35 mol ³He = (1/2)^x Taking the natural logarithm of both sides: ln(5.25/6.35) = -x ln(2) Solving for x: x = ln(5.25/6.35) / ln(2) ≈ 3.218 Therefore, 3.218 half-lives have passed, corresponding to a total elapsed time of: 3.218 × 12.32 years ≈ 39.72 years Therefore, the container has been sealed for about 39.72 years, which closest to 14.1 years (D).

A Pure Sample of Tritium, 3H, Was Prepared and Sealed

A Pure Sample of Tritium, ³H, Was Prepared and Sealed