Question

How do you determine the total mass of an original 28.0-milligram sample of Po-210 that remains unchanged after 414 days?

Answer 1

Given the 138.4 day half-life of the radioisotope `3.5*mg` of `""^210Po` will remain.

Explanation:

Given the boundary conditions of the problem it was SPECIFIED that the mass of `""^210Po` remained unchanged. I acknowledge, however, that this is a radioactive decay problem, and `""^210Po` is a screaming hot isotope and `alpha-"emitter"` with a half-life of 138.4 days; these data SHOULD have been supplied with the problem.

And so your polonium isotope has experienced 3 half-lives.........And there is thus `(1/2)^3=1/8` of the original mass, i.e. `3.5*mg`.

Note that I think this was the first radioisotope isolated by Marie Curie who named it after her native Poland.