ok in my professors notes he calculates carbon 14 age in an example.
The problem goes like this:
Sample contains 110g carbon
sample produces 70 disintegrations per minute.
That is 0.7 disintegrations per minute.
T=(1/lambda)ln(N0/Nt)
Then he substitutes:
t=(1/1.209*10^-4/year)ln(1600/70)
I just want to know where did he get 1600 from?
No is 1600 disintegrations per minute, it was the disintegrations per minute in the original sample at the beginning.
What concerns me is the last two lines of your text notes..
sample produces 70 disintegrations per minute, that is .7 diintegrations per minute. Huh?
I wrote exactly what he had in his notes. so what should the actual t=? is everything else correct except the 1600? I have no examples in my book.
To understand where your professor got the value of 1600 in the calculation, we need to have some background knowledge about the carbon-14 dating method.
Carbon-14 (C-14) dating is a technique used to determine the age of ancient artifacts and fossils by measuring the amount of C-14 remaining in them. C-14 is a radioactive isotope of carbon that is naturally present in the atmosphere. It undergoes radioactive decay at a known rate, meaning it gradually decreases over time.
The equation your professor used for carbon-14 dating is as follows:
t = (1/λ) * ln(N₀/Nₜ)
In this equation:
- t represents the age of the sample in years
- λ is the decay constant for C-14, which is 1.209 × 10^-4 per year
- N₀ represents the initial amount of C-14 in the sample
- Nₜ represents the current amount of C-14 in the sample
Now, let's focus on the values you provided in the calculation:
- The sample contains 110g of carbon.
- It produces 70 disintegrations per minute, which can also be written as 0.7 disintegrations per minute (since they are equivalent).
To get the value of N₀, you need to determine the initial amount of C-14 in the sample. This can be done by assuming that the amount of C-14 in living organisms, which is in equilibrium with the atmosphere, is constant. The fraction of C-14 in the atmosphere is about 1.3 × 10^-12, which means that for every 1 trillion atoms of carbon, approximately 1.3 atoms are C-14.
To calculate N₀, you need to convert the sample's mass of carbon (110g) into the number of atoms of C-14. Since the atomic mass of carbon is approximately 12 atomic mass units (AMU), you can divide the sample's mass by 12 to get the number of moles of carbon. Then, multiply the number of moles by Avogadro's constant to convert it into the number of individual carbon atoms, and then multiply by the fraction of C-14 in the atmosphere.
After finding N₀, you can plug it into the equation along with Nₜ (0.7 disintegrations per minute) and solve for t.
Now, back to your question about where your professor got the value of 1600. It seems that the value of 1600 is the ratio N₀/Nₜ used in the calculation. However, without further context or information about the problem, it is not clear how your professor arrived at that specific value. It is possible that it was provided as part of the problem statement or derived from additional information. If you have access to any additional information or context related to the problem, it might help clarify the reasoning behind the value of 1600.