Answer
There are necessary 200 days to drop the radiation level of strontium-85 to one-eighth of its original level.
Work Step by Step
1. After one half-life, the level of strontium-85 is dropped to one-half of its original level.
$[Strontium-85] = \frac{1}{2}[Strontium-85]_{initial}$
2. After the second half-life, the level of strontium-85 is dropped to one-fourth of its original level.
$[Strontium-85] = \frac{1}{2}(\frac{1}{2}[Strontium-85]_{initial}) = \frac{1}{4}[Strontium-85]_{initial}$
3. After the third half-life, the level of strontium-85 is dropped to one-eighth of its original level.
$[Strontium-85] = \frac{1}{2}(\frac{1}{4}[Strontium-85]_{initial}) = \frac{1}{8}[Strontium-85]_{initial}$
4. Since we have determined the number of half-lives (3), we can calculate how long will it take.
$3 half-lives \times \frac{65 days}{1half-life} = 200 days $