The activity of carbon 14 in living tissue is 15.3 disintegrations per minute per gram of carbon. The limit for reliable determination of age is based on carbon 14 is .10 disintegration per min per gram of carbon. Calculate the max age of a sample that can be dated accurately by radiocarbon dating. The half life is 5730 years.
If the half life is 5730 I get 0.123 years for k. The constant. How do I use the other information to get the max age of the sample?
No. ln(No/N) = kt is good only for first order AND in it's complete form is ln(No/N) = akt.
No = number of atoms initially
N = number of atoms at time t.
Note: usually number; however, dpm, concn, or other initial/final states work as well. In this case I used 15.3 for No since that is the original dpm (disintegrations/min) and 0.1 dpm since that is the smallest the problem states that can be reliably determined.
If t1/2 is in years, then k is in years^-1 and t is in years. If half life is in seconds, then k is in seconds^-1 and t is in seconds.
I don't agree with your value for k.
k = 0.693/t1/2 = 0.0001209 Yr^-1
If we can detect 0.1 dpm, then
ln(15.3/0.1) = kt and solve for t. The web states that 58,000 to 62,000 years can be reliable determined by rediocarbon dating. This is in that ball park.
Oh, okay. Do I always use that equation for any order rxn involving time? How about the units, would it be yrs^-1 or just years?
How do you know what number goes on the top and bottom for the disintegration?
To calculate the maximum age of a sample that can be accurately dated using radiocarbon dating, you can use the concept of exponential decay and the given information about carbon-14 activity and the limit for reliable determination of age.
The rate of decay of carbon-14 is described by the exponential decay formula:
N(t) = N₀ * e^(-kt)
Where:
N(t) = the amount of carbon-14 remaining at time t
N₀ = the initial amount of carbon-14
k = the decay constant
t = time in years
Given that the half-life of carbon-14 is 5730 years, we can determine the decay constant (k) as follows:
k = 0.693 / half-life
k = 0.693 / 5730
k ≈ 0.00012087
Now, we can use the information given in the question to solve for the maximum age (t). According to the question, the limit for reliable determination of age is 0.10 disintegration per minute per gram of carbon. Therefore, we can set up the following equation:
0.10 = 15.3 * e^(-0.00012087 * t)
To solve for t, we can take the natural logarithm (ln) of both sides of the equation:
ln(0.10) = ln(15.3 * e^(-0.00012087 * t))
Since ln(e^x) = x, the equation simplifies to:
ln(0.10) = ln(15.3) - 0.00012087 * t
Now, we can rearrange the equation to solve for t:
t = (ln(15.3) - ln(0.10)) / (-0.00012087)
By plugging in the values into the equation, you can calculate the maximum age of the sample that can be accurately dated using radiocarbon dating.