Respuesta :
Radioactive decay is characterized by the formula
[tex]N=(\frac{1}{2})^{\frac{t}{t_h}}N_0[/tex]Where N is the amount of the element remaining,
[tex]N_0\text{ is initial amount of the element}[/tex]t is the time taken to reduce the amount of the element to N and th is the half life of the element
In this case
[tex]N=\frac{N_0}{8}[/tex]And
[tex]th=3days=3\times24\times60\times60=2.6\times10^5\text{ s}[/tex]We need to find t
So we substitute the known values in the above equation
[tex]\frac{N_0}{8}=N_0\times(\frac{1}{2})^{\frac{t}{2.6\times10^5}}[/tex]Which is
[tex]\frac{1}{8}=(\frac{1}{2})^{\frac{t}{2.6\times10^5}}[/tex]Taking the log on both sides,
[tex]\log (\frac{1}{8})=-\log (8)=\frac{t}{2.6\times10^5}\log (\frac{1}{2})[/tex]Simplifying,
[tex]-0.9=\frac{-0.3\times t}{2.6\times10^5}[/tex]On rearranging and further simplifying we get,
[tex]t=1.15\times10^{-5}\text{ s}[/tex]Thus the time taken for fermium 253 to reduce to one-eight of its initial amount is
[tex]1.15\times10^{-5}\text{ s}[/tex]