An artifact contains one-fourth as much carbon-14 as the atmosphere. How old is the artifact? Use Figure 10-3 to answer this question.
dlap.gradpoint.com/dlap.ashx?cmd=getresource&entityid=12372948&path=content%2Fmedia%2F459431-472011-12118-PM-367894666.png&version=1
First, determine k
k = 0.693/half life = 0.693/5730 = ?
I looked up the half life on Google. from the link you listed
Then we must know how much C-14 is there. I looked up CO2 in the atmosphere in 2018 and found 0.04%. So there is 0.04/4 = 0.01 C-14 now (using 2018 as a standard. Does your problem tell you which year that was true? Probably not. Google says C-14 gives about 14 dpm (disintergrations per minute) so this sample must give 0.14 x 0.01 = 0.14.
ln (No/N) = kt
No = 14
N = 0.14
k from above
Solve for t in years.
Post your work if you get stuck.
To answer this question, we need to refer to Figure 10-3, which unfortunately cannot be accessed through text. However, I can help you understand the concept and the steps to solve the problem without referring to the specific figure.
Carbon-14 is an isotope of carbon that is commonly used for carbon dating to determine the age of artifacts or fossils. The concentration of carbon-14 in the atmosphere is relatively constant. When a living organism dies, it stops ingesting carbon-14, hence its concentration begins to decrease over time due to its radioactive decay.
In this case, the artifact contains one-fourth as much carbon-14 as the atmosphere. This indicates that the concentration of carbon-14 in the artifact is 1/4 of the concentration in the atmosphere.
To determine the age of the artifact, we need to compare the current concentration of carbon-14 in the artifact with the expected concentration in a living organism. Since the concentration of carbon-14 in the atmosphere is constant, we can assume that the concentration in a living organism is also constant.
If the artifact contains one-fourth of the carbon-14 as the atmosphere, it means that the artifact is approximately 1/4 as old as a living organism. Therefore, if we assume the average lifespan of a living organism is X years, the artifact would be X/4 years old.
Without Figure 10-3, we cannot provide you with a specific numerical value for the age of the artifact, but the general concept and approach to the problem should guide you in determining the approximate age. If you have access to the figure, it will provide specific values that can be used in the calculation.