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

`\% (A)/(A_0)=75.9\%`

Step-by-step 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:

`(A)/(A_0) =2^{-(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:

`(A)/(A_0) =2^{-(365years)/(1599years)\\\\(A)/(A_0) =0.759`

Thus, the percent is:

`\% (A)/(A_0)=0.759*100\%\\\\ \% (A)/(A_0)=75.9\%`

Best regards!