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By applying the <em>radioactive simple decay</em> model, we find that the <em>initial</em> quantity of the <em>radioactive</em> isotope is equal to approximately 5.63 grams.
<h3>How to determine the initial mass of a radioactive isotope</h3>
Mass of <em>radioactive</em> isotopes (m (t)), in grams, decay exponentially in time according to the following model:
(1)
Where:
- Initial mass, in grams
- t - Time, in years
- τ - Time constant, in years
The <em>time</em> constant can be found in terms of half-life:
τ = t'/㏑ 2
If we know that t' = 24100 yr, t = 1000 yr and m(t) = 5.4 g, then the initial mass of the <em>radioactive</em> isotope is:
τ = 24100 yr/㏑ 2
τ ≈ 34768.95 yr
By applying the <em>radioactive simple decay</em> model, we find that the <em>initial</em> quantity of the <em>radioactive</em> isotope is equal to approximately 5.63 grams.
To learn more on radioactive decay: brainly.com/question/1770619
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