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

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