Answer: 3,590 g
Step-by-step explanation:
Using the formula:
[tex]N = N_{0}e^{-kt}[/tex]
where
[tex]N =[/tex] remainder after a given time , that is
[tex]N = 7g[/tex]
[tex]N_{0} =[/tex] Original number of radium
[tex]N_{0}=?[/tex]
[tex]t = 4,653 years[/tex]
[tex]K = \frac{In2}{t^{\frac{1}{2}}}[/tex] , where [tex]t^{\frac{1}{2}}[/tex] is the half life , therefore :
[tex]K = \frac{0.6931}{517}[/tex] = 0.001341
substituting all into the formula [tex]N = N_{0}e^{-kt}[/tex] , we have :
[tex]7 = N_{0}e^{-0.001341(4653)}[/tex]
[tex]7 = N_{0}e^{-6.2382}[/tex]
[tex]7 = 0.001950N_{0}[/tex]
dividing through by 0.001950
[tex]N_{0} = 7/ 0.001950[/tex]
[tex]N_{0} =[/tex] [tex]3,589.74[/tex] g
Therefore , there are approximately 3,590g of radium at the beginning
