Radiocarbon dating is effective on specimens up to 40000 yea

Radiocarbon dating is effective on specimens up to 40,000 years old. In 1953, a nuclear chemist was trying to determine the age of some scrolls that were recently found. Carbon-14 has a half life of 5730 years. If he found 79.4% of the original carbon-14 still present, in about what year were the scrolls made?


The scrolls were made in about A.D. ______ . ?

Solution

Formula for decay constant = log2/half life = 0.693/5730 =0.0001209

exponential decay equation: N(t) = Noe^(-kt) where No is intial amt ;N(t) = final amt ; t = time; k =decay constant

N(t) =0.794No

0.794No = Noe^(-0.0001209t)

0.794 = e^(-0.0001209t)

take on natural log on both sides:

ln0.794 = -0.0001209t

t = 1907.95 years

Approxiamtely it took 1908 years i.e.year no. 3861