The heaviest known isotope of hydrogen is called tritium, $^3_1$H . It decays by beta emission, and has a half-life of 12.3 years. What fraction of a tritium sample will remain after 5.20 years

Question

Quizplus · Accepted Answer

To solve this problem we can use the radioactive decay formula:

N(t) = N0e^(-λt)

Where N(t) is the amount of tritium remaining after time t, N0 is the initial amount of tritium, λ is the decay constant (ln2/half-life), and t is the time elapsed.

We want to find the fraction of the sample that remains after 5.20 years, which is equivalent to finding N(5.20)/N0. Substituting the values given in the problem, we get:

N(5.20)/N0 = e^(-λt) = e^(-ln2/12.3 * 5.20) ≈ 0.746

Therefore, the best choice is B, which represents the fraction of the sample that remains after 5.20 years.

The Heaviest Known Isotope of Hydrogen Is Called Tritium 13^3_113​ H It Decays by Beta Emission, and Has a Half-Life

The Heaviest Known Isotope of Hydrogen Is Called Tritium $^3_1$ H It Decays by Beta Emission, and Has a Half-Life