The half-life of carbon 14 is 5730 years. if a 1 g sample of old carbon is 1/8 as radioactive as 1 g of a current sample, then the age of the old sample is about ___________years.
22,900
17,200
11,500
716
if I am correct, B. 17,200. I looked it up and this is what it said "b.) 17,200
if it takes 5730 years to be half then it takes 2*5730 years to be a quarter and 3*5730 years to be an eighth (2^3=8) so to get an 1/8 you need to half it 3 times and it takes 5730 years to half each time, thus 3*5730 ~ 17,200"
No problem.
To determine the age of the old carbon sample, we can use the concept of half-life. The half-life of carbon-14 is given as 5730 years.
Let's break down the information given in the question:
1 g of the old carbon sample is 1/8 as radioactive as 1 g of the current sample.
This means the amount of radioactivity in the old carbon sample is 1/8th of the current sample. Since the radioactivity of a substance decreases by half after each half-life, we can calculate the number of half-lives it took for the old carbon sample to reduce its radioactivity to 1/8th of the current sample.
1/8 = (1/2)^(n)
Where 'n' represents the number of half-lives.
To solve for 'n', we can take the logarithm of both sides:
log(1/8) = log((1/2)^(n))
Using the property of logarithms that log(a^b) = b * log(a), we can simplify:
-3 = n * log(1/2)
Dividing both sides by log(1/2):
n = -3 / log(1/2)
Calculating the value:
n ≈ 4.807
Since we cannot have a fraction of a half-life, we round this value to the nearest whole number, which is 5.
Now we can determine the age of the old carbon sample:
age = number of half-lives * half-life
age = 5 * 5730 years
age ≈ 28,650 years
Therefore, the age of the old carbon sample is approximately 28,650 years.
None of the given options match the calculated value exactly. However, the closest option is 22,900 years.