The half-life of a radioactive nucleus Radium of mass number 226 and atomic number 88 1.6×10³ years. If a sample initially contains 3.00×10^16 Such nuclei. Determine the initial activities in curries?

To determine the initial activity of the sample, we first need to calculate the decay constant (λ) using the formula:

λ = 0.693 / T1/2

where T1/2 is the half-life of the nucleus. Given that the half-life of Radium-226 is 1.6×10³ years, we can calculate the decay constant:

λ = 0.693 / 1.6×10³ = 4.33×10^-4 years^-1

Next, we can calculate the initial activity (A0) of the sample using the formula:

A0 = λ * N0

where N0 is the initial number of radioactive nuclei in the sample. Given that the sample initially contains 3.00×10^16 Radium-226 nuclei, we can calculate the initial activity:

A0 = 4.33×10^-4 * 3.00×10^16 = 1.30×10^13 curies

Therefore, the initial activity of the sample containing 3.00×10^16 Radium-226 nuclei is 1.30×10^13 curies.