Question

the half life of polonium is 139 days. you have a brand new sample of polonium that will not be useful to you after 80% of the material hasdistegraded. For how many days will you be able to use the polonium?

Answer 1

The half-life of Po is 139 days, so its decay rate is

0.5 = e^(139k)  ==>  k = ln(0.5)/139

After some time t, 80% of the material will have decayed and you'll be left with a sample 20% of its original mass:

0.2 = e^(kt)  ==>  t = ln(0.2)/k = ln(0.2)/ln(0.5) * 139 = 322.748

so your sample is usable for about 323 days.