Please show your solution on a paper using the formulas on the picture. Thank you so much! Question:Fossilized tortoise shell was discovered in an ancient cave dwelling in northern Philippines. A sample of the shell has a specific activity (which is equivalent to Nt) of 4.12 disintegration per minute per gram (d/min-g). If the ratio of C-12 and C-14 in living organisms results to 17.5 d/min-g (which is equivalent to N0), how old is the fossil given that the half-life of C-14 is 5730 years? The rate of radioactive decay follows first-order kinetics where the rate of decay isproportional to the number of radioactive nuclei (N) in the sample as expressed in Equation 6.1where k is called the nuclear decay constant.Rate = kN (Equation 6.1)Equation 6.1 can be transformed into Equation 6.2 where No is the initial number of nuclei at initialtime, time =0, and N₁ is the number of nuclei after time a certain time interval, t.In = -kt (Equation 6.2)NtNoA more useful way of determining the rate of radioactive decay is by determining the half-life of a radioisotope. Half-life (t₁/2) is the time required for half of any given quantity of radioactivesubstance to decay. Each radioisotope has a characteristic half-life. For example, cobalt-60which is used for cancer radiation therapy has a half-life of 5.3 years. So for a 1.00 g sample ofcobalt-60 it will take 5.3 years before its amount is reduced to 0.500 g and 10.6 yrs to 0.250g andso on and so forth. Equation 6.3 gives the general equation for the half-life of any radioactivesubstance while Equation 6.4 is the general formula in calculating the amount of remainingsubstance after n half-lives.0.693t1/2 =(Equation 6.3)Nt= (1/2) No (Equation 6.4)

In the given question we have to calculate the complete life of Fossil fuel, first of all, we have…

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Chemistry

9th Edition

ISBN:9781133611097

Author:Steven S. Zumdahl

Publisher:Steven S. Zumdahl

Chapter19: The Nucleus: A Chemist's View

Section: Chapter Questions

Problem 3RQ

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Please show your solution on a paper using the formulas on the picture. Thank you so much!

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Fossilized tortoise shell was discovered in an ancient cave dwelling in northern Philippines. A sample of the shell has a specific activity (which is equivalent to Nt) of 4.12 disintegration per minute per gram (d/min-g). If the ratio of C-12 and C-14 in living organisms results to 17.5 d/min-g (which is equivalent to N0), how old is the fossil given that the half-life of C-14 is 5730 years?

The rate of radioactive decay follows first-order kinetics where the rate of decay is
proportional to the number of radioactive nuclei (N) in the sample as expressed in Equation 6.1
where k is called the nuclear decay constant.
Rate = kN (Equation 6.1)
Equation 6.1 can be transformed into Equation 6.2 where No is the initial number of nuclei at initial
time, time =0, and N₁ is the number of nuclei after time a certain time interval, t.
In = -kt (Equation 6.2)
Nt
No
A more useful way of determining the rate of radioactive decay is by determining the half-
life of a radioisotope. Half-life (t₁/2) is the time required for half of any given quantity of radioactive
substance to decay. Each radioisotope has a characteristic half-life. For example, cobalt-60
which is used for cancer radiation therapy has a half-life of 5.3 years. So for a 1.00 g sample of
cobalt-60 it will take 5.3 years before its amount is reduced to 0.500 g and 10.6 yrs to 0.250g and
so on and so forth. Equation 6.3 gives the general equation for the half-life of any radioactive
substance while Equation 6.4 is the general formula in calculating the amount of remaining
substance after n half-lives.
0.693
t1/2 =
(Equation 6.3)
Nt= (1/2) No (Equation 6.4)

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