A bone fragment has lost 75% of its original carbon-14. What is the age of the bone fragment?
My answer is about 11 000 years but I don't know if its right
I obtained about 11,000 (11,466 but that's too many significant figures) years, too, so you probably did it right.
To find the age of the bone fragment, we can use the concept of half-life in radiocarbon dating.
Carbon-14 has a known half-life of approximately 5730 years, which means that every 5730 years, half of the carbon-14 in a sample will decay.
Since the bone fragment has lost 75% of its original carbon-14, it means that only 25% (or 1/4) of the original carbon-14 remains. In other words, the remaining carbon-14 is 25% of what the bone originally had.
To calculate the age, we need to determine how many half-lives have passed to get to 25% of the original carbon-14.
Using the formula
age = number of half-lives * half-life period,
we can calculate the age of the bone fragment.
Let's break it down step by step:
1. Calculate the number of half-lives that have passed.
To find this, we can use the following formula:
(number of half-lives)^2 = remaining carbon-14 / original carbon-14
In this case, the remaining carbon-14 is 25% of the original, so the above formula becomes:
(number of half-lives)^2 = 0.25
Taking the square root of both sides, we get:
number of half-lives = √(0.25)
number of half-lives = 0.5
2. Calculate the age using the number of half-lives and the half-life period.
The age can be calculated by multiplying the number of half-lives by the half-life period.
age = number of half-lives * half-life period
age = 0.5 * 5730 years
age ≈ 2865 years
So, according to the given information, the age of the bone fragment would be approximately 2865 years. Note that this is an approximation and may not be exactly 11,000 years.