The half life

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives?

Correct result:

m₃ =  18.125 g

Solution:

$$\begin{gathered} m_0=145\text{ g } \\ q=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ {m}_3=m_0\cdot q^3=145\cdot 0.5^3={\displaystyle \frac{145}{8}}={\displaystyle \frac{145}{8}}\text{ g}=18.125\text{ g} \end{gathered}$$

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