Given the remaining quantity after the given time and the half-life, the initial quantity or original mass of the sample is 32g.
Option A) is the correct answer.
What was the mass of the original sample?
Half-life is simply the amount of time it takes a given quantity to decrease to half of its initial value.
Using the expression:
[tex]N_{(t)} = N_{0}\frac{1}{2}^{\frac{t}{t_{\frac{1}{2} }} }[/tex]
Given the data in the question;
- Remaining quantity Nt = 1.0g
- time t = 40 days
- Half life t(1/2) = 8.07 days
[tex]N_{(t)} = N_{0}\frac{1}{2}^{\frac{t}{t_{\frac{1}{2} }} }[/tex]
[tex]1.0g = N_{0} * (0.5)^{40days/8.07days}\\\\1.0g = N_{0} * (0.5)^{4.95662949}\\\\1.0g = N_{0} * 0.0322037055\\\\N_{0} = \frac{1.0g}{0.0322037055} \\\\N_{0} = 31.05g = 32g[/tex]
Therefore, given the remaining quantity after the given time and the half-life, the initial quantity or original mass of the sample is 32g.
Option A) is the correct answer.
Learn more about half-life here: https://brainly.com/question/22691620
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