Tritium is radioactive with a half-life of 12.33 years decaying into 3He with low-energy electron emission.If we have a sample of 3.00 x 10¹⁸ tritium atoms,what is its activity in decays/second? (1 year = 3.15 x 10⁷ s)

Question

Quizplus · Accepted Answer

First, we need to calculate the decay constant, λ, using the half-life given:

t1/2 = 12.33 years = 12.33 x 3.15 x 10^7 s/year ≈ 3.89 x 10^8 s

λ = ln2 / t1/2 ≈ 1.78 x 10^-9 s^-1

The activity, A, is defined as the number of decays per second, so we can use the following equation:

A = λN

where N is the number of radioactive nuclei. Substituting the given values, we get:

A = (1.78 x 10^-9 s^-1) x (3.00 x 10^21 nuclei) ≈ 5.35 x 10^9 decays/second

Therefore, the best choice is B, 5.35 x 10^19/second.

Tritium Is Radioactive with a Half-Life of 12