The half-life of polonium-218 is 3 min. if you start with 16 mg, how long will it be before only 1.0 mg remains?

The decay equation is of the form

where
m(t) = the mass remaining after t minutes
m₀ =  the initial mass
k = constant

Because the half-life is 3 minutes, therefore

Therefore
-3k = ln(0.5)
k = ln(0.5)/(-3) = 0.231

Because m₀ = 16 mg, the time, t, for the mass to decay to 1.0 mg is given by


22 min (nearest integer)