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 1.91 × 10¹⁸ tritium atoms,what is its activity in decays/second? (1 year = 3.15 × 10⁷ s)

Question

Quizplus · Accepted Answer

First, we need to calculate the lambda (decay constant) for tritium:

lambda = ln(2)/half-life = ln(2)/12.33 years = 0.0563/year

Next, we need to convert the sample size from atoms to moles:

n = 1.91 x 10^18 atoms / 6.022 x 10^23 atoms/mol = 3.18 x 10^-6 mol

Now, we can use the radioactive decay law to calculate the activity (decay rate) of the sample:

A = lambda * N = lambda * N_A * n

where N_A is Avogadro's number (6.022 x 10^23 mol^-1)

A = 0.0563/year * 6.022 x 10^23 mol^-1 * 3.18 x 10^-6 mol = 1.08 x 10^15 decays/year

Finally, we need to convert the activity from years to seconds:

A = 1.08 x 10^15 decays/year * (1 year / 3.15 x 10^7 s) = 3.41 x 10^9 decays/s

Therefore, the answer is B) 3.41E+9 decays/second.

Tritium Is Radioactive with a Half-Life of 12