1The Dead Sea Scrolls are documents that contain some of the

1The Dead Sea Scrolls are documents that contain some of the oldest known texts of parts of the Hebrew bible. They were discovered between 1947 and 1956 in several caves near the ruins of the ancient settlement of Khirbet Qumran on the northwest shore of the Dead Sea. Archeologists determine that a sample taken from the scrolls contains 79.10% of the carbon-14 that it originally contained. (The half-life of carbon-14 is 5730 years.) Estimate the age of the Dead Sea Scrolls. (Round the growth factor to eight decimal numbers. Round your answer to the nearest year.) 2A nuclear power plant produces radioactive plutonium-239, which has a half-life of 24,110 years. Because of its long half-life, plutonium-239 must be disposed of safely. How long does it take 100 grams of radioactive waste from the nuclear power plant to decay to 10 grams? (Round the growth factor to eight decimal numbers. Round your answer to the nearest year.)

Solution

1) Decay constant = 0.693/5730 =0.00012094

N(t) = Noe^-kt

N(t) = 79.10% of No

N(t) = 0.7910No

0.7910 = e^(-0.00012094t)

ln(0.7910) = -0.00012094t

t = 1938.62 = 1939 years