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A radioactive element disintegrates at a rate proportional to the quantity of substance $\mathrm{Q}$ present at any time $\mathrm{t}$. What is the differential equation of the disintegration?
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The correct answer is:
$\frac{d Q}{d t}=-k Q, k>0$
A radioactive element disintegrates at a rate proportional to the quantity of substance $Q$ present at any time $\mathrm{t}$.
$\Rightarrow \quad \frac{\mathrm{dQ}}{\mathrm{dt}} \propto-\mathrm{Q}$
$\Rightarrow \frac{\mathrm{dQ}}{\mathrm{dt}}=-\mathrm{kQ}, \mathrm{k}>0$ is a constant.
This is required differential equation.
$\Rightarrow \quad \frac{\mathrm{dQ}}{\mathrm{dt}} \propto-\mathrm{Q}$
$\Rightarrow \frac{\mathrm{dQ}}{\mathrm{dt}}=-\mathrm{kQ}, \mathrm{k}>0$ is a constant.
This is required differential equation.
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