Thank you for visiting The half life of a radioactive substance is 39 4 years a Find the exponential decay model for this substance b How long will it. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The exponential decay model for a radioactive substance is N(t) =[tex]Nâ‚€e^(-t(ln(2)/39.4))[/tex].
To find how long it will take for a sample of 500 grams to decay to 400 grams, we can substitute N(t) = 400 and
Nâ‚€ = 500 into the decay model and solve for t, which is approximately 0.2236 years.
Radioactive decay is a process in which the number of atoms of a radioactive substance decreases over time. The exponential decay model for a radioactive substance is given by the formula N(t) = [tex]Nâ‚€e^(-kt)[/tex], where N(t) is the amount of substance at time t, Nâ‚€ is the initial amount of substance, k is the decay constant, and e is the base of the natural logarithm (approximately 2.71828).
In this case, the half-life of the substance is 39.4 years, which means that Nâ‚€/2 = [tex]Nâ‚€e^(-k*39.4)[/tex].
Solving this equation for k, we find k = ln(2)/39.4.
So, the exponential decay model for this substance is N(t) =[tex]Nâ‚€e^(-t(ln(2)/39.4))[/tex].
To find how long it will take for a sample of 500 grams to decay to 400 grams, we can substitute N(t) = 400 and
Nâ‚€ = 500 into the decay model and solve for t.
We get [tex]e^(-t(ln(2)/39.4))[/tex] = 400/500.
Taking the natural logarithm of both sides and solving for t, we find t ≈ 0.2236 years.
The third part of the question is incomplete.
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