Radium-221 has a half-life of 30 sec. How long will it take for 96% of a sample to decay?

We can calculate how long the decay by using the half-life equation. It is expressed as:

A = Ao e^-kt

where A is the amount left at t years, Ao is the initial concentration, and k is a constant.

From the half-life data, we can calculate for k.

1/2 (Ao) = Ao e^-k (30)

k = 0.023

0.04Ao = Ao e^0.023 (t)

t = 140 sec