Tritium (³H)has a half-life of 12.3 years and releases 0.018 6 MeV energy per decay.What is the activity of a 1.4-gram sample of tritium? (N_A = 6.02 × 10²³ mol^-1,1 year = 3.16 × 10⁷ s,1 MeV = 1.6 × 10^-13 J,and m_t = 3.016 05 u)

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the number of tritium nuclei in a 1.4-gram sample of tritium:

n = (m/M) * N_A

where m is the mass of the sample (1.4 g), M is the molar mass of tritium (3.01605 g/mol), and N_A is Avogadro's number (6.02 x 10^23 mol^-1)

n = (1.4/3.01605) * 6.02 x 10^23 = 2.807 x 10^23 tritium nuclei

The activity (A) is given by:

A = λ * N

where λ is the decay constant, and N is the number of radioactive nuclei.

The decay constant (λ) is related to the half-life (t½) by:

λ = ln(2)/t½

λ = ln(2)/12.3 years = 0.0563 years^-1 = 1.78 x 10^-9 s^-1

Therefore,

A = (1.78 x 10^-9 s^-1) * (2.807 x 10^23 nuclei) = 5.0 x 10^14 Bq

So the best choice is C, which gives the correct activity in Bq.

Tritium (3H)has a Half-Life of 12

Tritium (³H)has a Half-Life of 12