In this problem, we are being asked to** determine the mass of Strontium-90 remaining** when after three half-lives have passed the 50.0 g of sample.

Recall that ** radioactive/nuclear decay of isotopes** follows first-order kinetics, and the integrated rate law for first-order reactions is:

$\overline{){\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{N}\mathbf{\right]}}_{{\mathbf{0}}}}$

where:

**[N] _{t}** = concentration at time t

**k** = decay constant

**t** = time

**[N] _{0}** = initial concentration.

Also, recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a first-order reaction is given by:

$\overline{){\mathbf{k}}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{{\mathbf{t}}_{\mathbf{1}\mathbf{/}\mathbf{2}}}}$

Decay of a 10.0-g sample of strontium-90 (t_{1/2} = 28.8 yr).The 10 x 10 grids show how much of the radioactive isotope remains aftervarious amounts of time.

If we start with a 50.0-g sample, how much of it remains after three half-lives have passed?