Question
Carbon-14 has a half-life of 5700 years. In a living organism, the ratio of radioactive carbon-14 to
ordinary carbon remains fairly constant during the lifetime of the organism. After the organism’s
death no new carbon is integrated into the organism’s remains, so the proportion of carbon -14 in the
remains decreases according to the law of exponential chance. The variable of interest here is the
percent the original amount of carbon-14 present in the organism’s remains.
a) Find the exact value of k for the decay equation for carbon-14.
b) If a painting attributed to Vermeer (1632-1675) was painted 5 years before his death,
approximately what percentage of carbon-14 should it contain? Round off your answer to the nearest tenth of a percent.
c) The painting was declared a forgery because it contained 99.5% of its original carbon-14. Based
on the law of exponential decay, find the true age of the painting. Round off your answer to the nearest year.
ordinary carbon remains fairly constant during the lifetime of the organism. After the organism’s
death no new carbon is integrated into the organism’s remains, so the proportion of carbon -14 in the
remains decreases according to the law of exponential chance. The variable of interest here is the
percent the original amount of carbon-14 present in the organism’s remains.
a) Find the exact value of k for the decay equation for carbon-14.
b) If a painting attributed to Vermeer (1632-1675) was painted 5 years before his death,
approximately what percentage of carbon-14 should it contain? Round off your answer to the nearest tenth of a percent.
c) The painting was declared a forgery because it contained 99.5% of its original carbon-14. Based
on the law of exponential decay, find the true age of the painting. Round off your answer to the nearest year.
Answers
Steve
A(t) = Ao * 2^(-t/5700)
If you want that to use e instead of 2, then since 2 = e^ln2,
A(t) = Ao * e^(-ln2/5700 * t)
and k = ln2/5700.
Now just plug in your numbers to answer the other questions.
If you want that to use e instead of 2, then since 2 = e^ln2,
A(t) = Ao * e^(-ln2/5700 * t)
and k = ln2/5700.
Now just plug in your numbers to answer the other questions.
Cascaval
It cannot be determined, since carbon dating is very inaccurate
Anonymous
such