If a sample contains 70g of Carbon 14 and 70g of Nitrogen 14, how many half lives has it undergone? (show all of your work)
153
45
To determine the number of half-lives that the sample has undergone, we need to compare the amount of Carbon-14 (C-14) to the amount of Nitrogen-14 (N-14) in the sample.
Each time one half-life passes, half of the C-14 atoms will decay into N-14 atoms. So, the ratio of C-14 to N-14 in the sample will change as the number of half-lives increases.
Let's start by comparing the initial amount of C-14 to N-14 in the sample:
Initial C-14 = 70g
Initial N-14 = 70g
Now, we need to determine the atomic mass of C-14 and N-14:
Atomic mass of C-14 = 12g/mol + 14g/mol = 26g/mol
Atomic mass of N-14 = 14g/mol
Next, we calculate the number of moles for each isotope:
Moles of C-14 = Initial C-14 / Atomic mass of C-14
= 70g / 26g/mol
= 2.692 moles
Moles of N-14 = Initial N-14 / Atomic mass of N-14
= 70g / 14g/mol
= 5 moles
Now, we compare the moles of C-14 to N-14:
Moles of N-14 = 2^(number of half-lives) * Moles of C-14
Let's substitute the values and solve for the number of half-lives:
5 moles = 2^(number of half-lives) * 2.692 moles
Dividing both sides of the equation by 2.692 moles:
5 / 2.692 = 2^(number of half-lives)
Taking the logarithm base 2 of both sides:
log2(5 / 2.692) = number of half-lives
Using a calculator:
number of half-lives ≈ log2(1.857) ≈ 0.896
Since the number of half-lives must be a whole number, we can round down to the nearest whole number. Therefore, the sample has undergone approximately 0 complete half-lives.
Please note that the result of approximately 0 half-lives indicates that the sample has not yet experienced any appreciable decay of C-14 atoms into N-14 atoms.