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?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.