Radioactive decay

A type of radioactive element has a mass of 1.125 grams. Upon analysis, he is found to be 405 years old. If this radioactive element decays by half every 45 years, find how many grams of this radioactive element there were 405 years ago.

Correct answer:

m₀ =  576 g

Step-by-step explanation:

$$\begin{gathered} m=1.125\text{g} \\ T=45\text{y} \\ t=405\text{y} \\ n=t/T=405/45=9 \\ m=m_0\cdot 0.5^n \\ r=0.5^n=0.5^9=\frac{1}{512}\doteq 0.002 \\ {m}_0=\frac{m}{r}=\frac{1.125}{0.002}=576\text{g} \end{gathered}$$

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