By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.
How to determine the initial mass of a radioactive isotope
Mass of radioactive isotopes (m (t)), in grams, decay exponentially in time according to the following model:
[tex]m(t) = m_{o}\cdot e^{-t/\tau}[/tex] (1)
Where:
- [tex]m_{o}[/tex] - Initial mass, in grams
- t - Time, in years
- τ - Time constant, in years
The time 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 radioactive isotope is:
τ = 24100 yr/㏑ 2
τ ≈ 34768.95 yr
[tex]5.4 = m_{o}\cdot e^{-1000/24100}[/tex]
[tex]m_{o} = 5.629\,g[/tex]
By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.
To learn more on radioactive decay: https://brainly.com/question/1770619
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