a certain radioactive element has a half life of 31.2 years. in how many years will contamination reach 32% of the original contamination?
how many half lives in 32%
(1/2)^n = .32
n log .5 = log .32
n = -.495 / -.301 = 1.64 half lives
1.64 * 31.2 = ?
So the answer would be 51.168 years to get to 32% contamination?
To determine the number of years it will take for the contamination to reach 32% of the original contamination, we need to use the concept of half-life. The half-life of a radioactive element refers to the time it takes for half of the initial material to decay.
In this case, since we know the half-life of the radioactive element is 31.2 years, we can use this information to calculate the number of half-lives it will take for the contamination to reduce to 32% of its original value.
To find the number of half-lives required, we can use the formula:
Number of half-lives = (log(Percentage remaining) / log(0.5))
Let's calculate it:
Number of half-lives = (log(0.32) / log(0.5)) ≈ 2.063
Since the number of half-lives should be a whole number, we can round up to the nearest whole number, which is 3. This indicates that it will take 3 half-lives for the contamination to reach 32% of the original contamination.
Now, we need to multiply the half-life by the number of half-lives to find the total time it will take:
Total time = Half-life × Number of half-lives = 31.2 years × 3 = 93.6 years
Therefore, it will take approximately 93.6 years for the contamination to reach 32% of the original contamination.