(1) One issue confronting the use of 14C decay (half-life of 5760 years) to date
ID: 805968 • Letter: #
Question
(1)
One issue confronting the use of 14C decay (half-life of 5760 years) to date materials is that of obtaining a standard. One approach to this issue is found in the field of dendrochronology or using tree rings to determine age. Using this approach, tree materials dating back 10,000 years have been identified. Assuming you had a sample of such a tree in which the number of decay events was 17.0 decays per minute before decomposition, what would the decays per minute be in the present day?
[14C] = ???
(2) A convenient source of gamma rays for radiation chemistry research is 60Co, which undergoes the following decay process: 60/27Co?60/28Ni+??+?. The half-life of 60Co is 1.910^3 days.
What is the rate constant for the decay process?
How long will it take for a sample of 60Co to decay to half of its original concentration?
(3) Bananas are somewhat radioactive due to the presence of substantial amounts of potassium. Potassium-40 decays by two different paths:
40/19K?40/20Ca+??(89.3%)
40/19K?40/18Ar+?+(10.7%)
The half-life for potassium decay is 1.310^9 years.
Determine the rate constant for the first channel.
Determine the rate constant for the second channel.
(4)
The bimolecular reaction of chlorine monoxide can result in the formation of three different combinations of products or product channels (the rate constant for each reaction is indicated):
ClO?(g)+ClO?(g)?Cl2(g)+O2(g)k=2.9106
ClO?(g)+ClO?(g)?ClOO?(g)+Cl?(g)k=4.8106
ClO?(g)+ClO?(g)?OClO?(g)+Cl?(g)k=2.1106
Determine the quantum yield for the first product channel.
Determine the quantum yield for the second product channel.
Determine the quantum yield for the third product channel.
Explanation / Answer
(1) Crbon dating is a pseudo first order reaction. So,
using first order kinetics,
k = 0.693/t1/2
t1/2 = 5760 years
k = 0.693/ 5760 = 1.203 E-4
A= Ao x e^(-kt)
Ao = 17 decay per minute
t = 10000years
A = 17 x e^(-1.203E-4 x 10,000) = 17 x 0.3 = 5.1 decays per minute in present day.
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