Nuclear physics Radioactivity 90Sr has a half life of 28.5y. It is chemically similar to Ca and enters the body through the food  chain and collects in bones. It is a serious health hazard. How long in (years) will it take for    99.99% of Sr released in a nuclear reactor accident     to disappear?
 A: If initial mass is $M$. Amount remaining after $n$ half lives is $M/2^{n}$. 
Ask yourself, How much remains after 99.99% is gone? 
Equate. 
A: Pratik's point was a good one, though perhaps not the most helpful.
The decay of a radioactive material means that the amount of time for any specific percentage of a quantity of material to decay is constant.  That is, in this case,
$0.0001 N_0 = N_0 e^{-\lambda t}$
$t = -\frac{\ln(0.0001)}{\lambda}$
where $\lambda$ is called the decay constant.  In this case we have
$t \approx 379 \mbox{years}$

What you really should care about is the effect of this material.  When making these sorts of calculations for accident analysis, engineers consider, a huge variety of factors such as:


*

*amount of fuel in reactor,

*original composition of fuel,

*history of fuel (reactor operation),

*relative liklihood of different types of accident,

*relative liklihood of the release of refractory products (material from the core),

*likely percent of refractory products released to the environment,

*relative liklihood of dispersion of various refractory products (considering half-life, air bouyancy, diffusion factors, etc.),

*potential containment measures and all of the possibilities that go into their success or failure,

*decay chains of environmental contaminants

*environmental vectors for human exposure

*relative effect of various levels of exposure

*relative effect of type (inhalation, consumption, skin, etc.) of exposure

*etc., etc.


There is an entire field known as probabilistic risk assesment that examines these sorts of questions and debates the relative weights that should be placed on them.  I am not a PRA expert, but I have some experience with the field.
That being said, we, unfortunately, have some real data with which we can work.  In the case of Fukushima, the level of ${}^90$Sr in seawater some 7 months after the accident was less than $0.03 Bq/cm^3$; see this article.  Another source gives a value of 195 Bq.  This equates to about $4 \times 10^{-11}$ grams... not very much.  Considering that the deposition fraction (the amount that gets into bones once consumed/inhaled) is about 0.12, these quantities are quite minimal.
In short, it's not something you need to lose sleep over.
