The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 11 percent of the original amount absorbed remains?
To calculate the number of years it takes until only 11 percent of the original amount of radioactive strontium-90 remains, we can use the concept of half-life.
The half-life of radioactive strontium-90 is approximately 31 years, which means that after each 31-year period, the amount of radioactive strontium-90 is reduced by half.
To find out how many half-lives it takes for only 11 percent of the original amount to remain, we can use the following formula:
(number of half-lives) = (log(remaining percentage) / log(0.5))
In this case, the remaining percentage is 11 percent or 0.11.
(number of half-lives) = (log(0.11) / log(0.5))
Calculating this using a calculator or any scientific calculator that supports logarithmic functions, we find:
(number of half-lives) ≈ 3.56
Since we cannot have a fraction of a half-life, we need to round up to the nearest whole number. Therefore, it takes approximately 4 half-lives for only 11 percent of the original amount of radioactive strontium-90 to remain.
Now, to find the total number of years it takes, we multiply the number of half-lives by the length of each half-life:
(total number of years) = (number of half-lives) × (length of each half-life)
(total number of years) = 4 × 31 years
Thus, it takes approximately 124 years until only 11 percent of the original amount absorbed remains.