Question

Dinosaur fossils are too old to be reliably dated using carbon-14, which has a half-life of about 5730 years. Suppose we had a 66 million year old dinosaur fossit. How much of the living dinosaur's 14c would be remaining today? (Round your agswer to flve decimal places.) % Suppose the minimum detectable amount is O.7 %. What is the maximum age of a fossil that we could date using 14c7 (Round your answer to the nearest integer) Need Help? Read it Talk to a Tutor

Answer 1

Que) Hoge No. Date I I Dinosaur tassits are too old to be keliably dated using carbon - 14 which has a half-life. of about 5730 years, suppose we had a GG million Year old dinosaur fossit. How much of the I living dinosaur's the would be remaining I today ? The helf life of carbon - 14 is approximately 5730 years, Carbon dating is used to determine the age of biological artifacts upto 50,000 years old and this technique will not work on oddes fossils like dinosauks alleged to be mittions of years old Now, the Half life of the substance is equal to the length of time taken for half of the substance to decay. i.e if length of time is known then the amount of the substance that remains M(t) = M.X2 41 Where tis amount of time and his the half life of carbon - 14 - Assume that cas mittion years ago, this dinosaur fossil had 100% of its carbon-14. Thus, evaluating this function for an initial amount of tooiſ would give the percentage that remain _ Mt) = Loox 2-660000075730 ( GG mittions = 66X 106 ² Loox2-11518-32 - JOOXO - m(t)=0 because when we take 2 to this very small number it is effectively zero,

Page No. 2) Date 1 1 Hence, this can be difficult to calculate This is why we can't use 'Carbon dating to I approximate the age of these fossils because I we can't detect such a very small amount suppose the minimum detectable amount is 0.7% What is the maximum age of a fossil that we could date using the 1402 - giren h=5730 Thus, the substance to decay 0.7% of its Loliginal amount can be calculated by wing some formula which we use eacties .. te MCt = M X 2 2 ) cuo can once again begin with initial value of too% and we solve it for t to this we we need to use logarithms to bring down the exponent to allow us the variable which are isolate d

Thus, M (t) = M. x i 0.7 = 1oox - +/5730 0.007 = 2-1/5730 I taking log on both side we get In (0.007) = lon 2-t/5730 I to 0.007= -t to 2 (idnats atna) 5730 | 2 | = - 5730 (2007) t = 4102021 Therefore it would take approximately 44020 years for an amount of carbon - 14 to decay to this amount which would be a Prediction for the maximum are of this fossil.