Question

The radioactive waste strontium-90 has a half-life of 28 years. How long must a sample of strontium-90 be stored to ensure that only 1/16 of the original sample remains as radioactive strontium-90?

Answer 1

To ensure that only 1/16 of the original strontium-90 remains, it must be stored for a period of 112 years, which is four half-lives of the isotope.

Step-by-step explanation:

Radioactive Decay of Strontium-90

Strontium-90 is a radioactive isotope with a half-life of 28 years. To determine how long it takes for only 1/16 of the original sample to remain, we need to calculate how many half-lives it takes to reach this fraction. After the first half-life, 1/2 of the original amount remains, after the second, 1/4 remains, after the third, 1/8 remains, and after the fourth half-life, 1/16 remains. Therefore, it takes four half-lives for only 1/16 of the original strontium-90 sample to remain. Multiplying the number of half-lives by the half-life duration gives us the total storage time required:

Storage time = Half-lives × Half-life duration

= 4 × 28 years

= 112 years.

So, a sample of strontium-90 must be stored for 112 years to ensure that only 1/16 of the original sample remains as radioactive strontium-90.