The half-life of 234U, uranium-234, is 2.52 105 yr. If 97.7% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?
? yr
To find the length of time that has elapsed, we need to use the concept of half-life.
The half-life of uranium-234 is given as 2.52 * 10^5 years. This means that after every half-life, the amount of uranium-234 remaining will be reduced by half.
In this case, 97.7% of the uranium in the original sample is present. This implies that 2.3% of the uranium-234 has decayed.
To determine the number of half-lives that have occurred, we can use the formula:
(number of half-lives) = (log(initial amount / final amount)) / (log(2))
Let's calculate the number of half-lives:
(number of half-lives) = (log(100% / 2.3%)) / (log(2))
(number of half-lives) = (log(100 / 2.3)) / (log(2))
(number of half-lives) ≈ 6.062
Since each half-life is 2.52 * 10^5 years, the total time elapsed is:
(total time elapsed) = (number of half-lives) * (half-life duration)
(total time elapsed) ≈ 6.062 * 2.52 * 10^5 years
Finally, to get the answer to the nearest thousand years, we round the result:
(total time elapsed) ≈ 15,256 years
Therefore, the length of time elapsed is approximately 15,256 years.