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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?
Anonymous
Mar 2
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?
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ChatGPT
Mar 2
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.
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.
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