The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5594 years. Suppose C'(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' = k = (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = years -kC. [1]: The New York Times, October 18, 1988.

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5594 years. Suppose C'(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C' = k = (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = years -kC. [1]: The New York Times, October 18, 1988.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter20: Kinetics

Section: Chapter Questions

Problem 20.88E

See similar textbooks

Similar questions

The radioactive isotope carbon-14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to stable carbon-12 at a rate proportional to the amount of carbon-14 present, with a half-life of 5550 years. Suppose C(t) is the amount of carbon-14 present at time t. (a) Find the value of the constant k in the differential equation C′=−kC. k= ? (b) In 1988 three teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained about 91 percent of the amount of carbon-14 contained in freshly made cloth of the same material[1]. How was old the Shroud of Turin in 1988, according to these data? Age = ? years [1]: The New York Times, October 18, 1988.
Consider an exponential decay function P(t) = P0e-lt, and let T denote its time constant. Show that, at t = T, the function P(t) decays to about onethird of its initial size. Conclude that the time constant is always larger than the half-life.
A research group discovers a new version of happyase, which they call happyase*, that catalyzes the chemical reaction: HAPPY↽⇀SAD The researchers begin to characterize the enzyme. The researchers determined the kcat of the enzyme to be 555 s-1. In a separate experiment with [Et] at 3.2 nM and [HAPPY] at 55 µM, the researchers find that ?0 is equal to 220 nM s−1. What is the measured ?m of happyase* for its substrate HAPPY?
DEQ: A fungal specie of cordyceps turns humanity into a zombie-like state. The rate of growth of a singlecordyceps was observed and was determined to be proportional to itself. If between noon and 2:00PM, the population triples, at what time, no controls being exerted, should the cordyceps becomes 100times what it was in noon?
Sucrose (C12H22O11)(C12H22O11), which is commonly known as table sugar, reacts in dilute acid solutions to form two simpler sugars, glucose and fructose, both of which have the formula C6H12O6C6H12O6. At 23 ∘C∘C and in 0.5 M HClM HCl, the following data were obtained for the disappearance of sucrose: Time (min)(min) C12H22O11(M)C12H22O11(M) 0 0.316 39 0.274 80 0.238 140 0.190 210 0.146 What is the rate constant?
What are the significance of the value of the slope, the value of the y-intercept, and the correlation coefficient to the determination of half-life?
Consider the reaction N₂O(g) →N₂(g)1/2O₂(g) with Au has catalyst (a) Is the gold a homogeneous or a heterogeneous catalyst?(b) On the same set of axes, sketch the reaction energy dia-grams for the catalyzed and the uncatalyzed reaction
A research group discovers a new version of happyase, which they call happyase*, that catalyzes the chemical reaction HAPPY ⇌ SAD. The researchers begin to characterize the enzyme. (a) In the first experiment, with [Et] at 4 nM, they find that the Vmax is 1.6 μM s−1. Based on this experiment, what is the kcat for happyase*? (Include appropriate units.) (b) In another experiment, with [Et] at 1 nM and [HAPPY] at 30 μM, the researchers find that V0 = 300 nM s−1. What is the measured Km of happyase* for its substrate HAPPY? (Include appropriate units.) (c) Further research shows that the purified happyase used in the first two experiments was actually contaminated with a reversible inhibitor called ANGER. When ANGER is carefully removed from the happyase preparation and the two experiments repeated, the measured Vmax in (a) is increased to 4.8 μM s−1, and the measured Km in (b) is now 15 μM. For the inhibitor ANGER, calculate the values of α and α′. . (d) Based on the information given…
The rate law for a reaction was reported as v= k,[A][B][C] with the molar concentrations in moles per cubic decimetre and the time in seconds. What are the units of k,?
A drug is infused intravenously (IV) for treatment of a particular disease. The infusion rate of the drug is k0 = 200 mg/hr. The volume of the body fluid V = 16 liters. The drug is excreted (removed) through the kidneys at rate ke = 0.3/hr, proportional to the concentration of the drug in the bodyfluids. How much is the maximum concentration of the drug in the body in the steady state in mg/l?
Technetium (Tc) is a by-product of the spontaneous fission of Uranium-238 and as such is of particular interest to the nuclear sector. The most common isotope is 99Tc which is unstable and decays by emission of a beta particle,with a half-life of t½ = 2.11 x 105 years. A 99Tc sample is characterised and is found to contain 0.1 mol of the radionuclide. Determine the time required for the amount of technetium to reduce by 1% of this value
Given the following plot for the decomposition of N2O5, calculate the frequency factor (A):