Answer to Question #257963 in Physics for Anand

Question

The half-life of an element I¹³¹ is 8.05 days. After how many days will only 10% of this element be left over?

Answer 1

The decay equation:

$$\frac{N}{N_0}=\frac{1}{2^{t/\tau}},\\\space\\ 2^{t/\tau}=\frac{N_0}N,\\\space\\ t=\tau·\frac{\ln(N_0/N)}{\ln2}=8.05·\frac{\ln(1/0.1)}{\ln2}=28.2\text{ days}.$$