Question

Need help regarding radioactive decay type of question

Answer 1

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:

$m(t) = m_{o}\cdot e^{-t/\tau}$     (1)

Where:

• $m_{o}$ - 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

$5.4 = m_{o}\cdot e^{-1000/24100}$

$m_{o} = 5.629\,g$

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: brainly.com/question/1770619

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