Question

Iron-59 has half-life of 45.1 days. How old is an iron nail if the Fr-59 content is 25% that of a new sample of iron

Answer 1

`m=0,25m_(0)\\ t=\?\\ \tau_{(1)/(2)}=45,1d\\\\ 0,25m_(0)=m_(0)*({(1)/(2))^{(t)/(45,1)}}\\\\ 0,25=(1)/(2)^{(t)/(45,1)}\\\\ log_(a){b}=c \ \ \Leftrightarrow \ \ a^(c)=b\\\\ (t)/(45,1)=log_{(1)/(2)}0,25\\\\ (t)/(45,1)=2\\\\ t=90,2d`