Question

The rate of decomposition of radioactive radium is proportional to the amount present at any time. The half-life of radioactive radium is 1599 years. What percent of a present amount will remain after 635 years

Answer 1

Answer:

$\% \frac{A}{A_0}=75.9\%$

Explanation:

Hello!

In this case, since the kinetics of the radioactive decay is assumed to be first-order, it is possible to use the following equation to quantify that change:

$\frac{A}{A_0} =2^{-\frac{t}{t_{1/2}}$

Thus, given the elapsed time, 635 years, and the half-life, 1599 years, we can compute the fraction of the present amount:

$\frac{A}{A_0} =2^{-\frac{365years}{1599years}\\\\\frac{A}{A_0} =0.759$

Thus, the percent is:

$\% \frac{A}{A_0}=0.759*100\%\\\\ \% \frac{A}{A_0}=75.9\%$

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