Question

Carbon Dating: All living organisms contain two isotopes (types) of carbon; carbon-12 ( 12C) and carbon-14 (14C). Carbon-12 is stable, meaning that its atoms do not decay. Carbon-14 however, is radioactive or unstable, meaning that an atom of carbon-14 may decay. It does this by throwing off an electron and thus transforming itself into Nitrogen 14. The ratio of carbon-14 to carbon-12 is the same for all living organisims, about 1/10, 000. However, once an organisim dies the carbon-14 begins to decay while the carbon-12 remains, thus lowering the carbon-14 to carbon-12 ratio. The half-life or carbon-14 is about 5700 years, meaning that a carbon-14 atom has a 50% chance of decaying over a 5700 year span. In other words, after 5700 years about half of the carbon14 you started with will be gone. This means that a sample of 14C decays at a rate that is proportional to the amount currently present. As you learned in section 6.5 of your text, and as discussed in class, this means that if the amount present at time t is given by Q(t), then Q(t) satisfies the differential equation Q 0 (t) = k Q(t).

(1) You also learned that the solutions to this equation have the form Q(t) = Q(0)e kt . (2) Suppose that your team has dug up some kind of animal bone, and you want to figure out how long ago that animal died. After analyzing the bone you determine the following:

1. The bone weighs 900 grams. 2. The bone is 65% 12C. 3. The ratio of 14C to 12C is 1/54, 000. Answer the following questions. Recall that to receive credit your answer must be supported by appropriate work. There should be no “number only” answers. At the very least, show the formula you are using to obtain your answer. 1. How many grams of 12C are present in the bone?

2. How many grams of 14C are present in the bone?

3. How many grams of 14C would have been present in the bone when the animal died?

4. How many grams of 14C would have been present in the bone 5700 years after the animal died?

5. Determine the constant k in equation (2) above as it pertains to this problem.

6. Write down a formula for Q(t), where Q(t) is the amount of 14C present in the bone t years after the animal died. Your formula should contain only two variables; The dependent variable Q and the independent variable t.

7. Using your formula, calculate the amount of 14C present in the bone 10,000 years after the animal died.

8. Based on your findings, is the bone more than 10,000 years old?

9. Using your formula, calculate the amount of 14C present in the bone 20,000 years after the animal died.

10. Based on your findings, is the bone more than 20,000 years old?

11. Calculate the age of the bone algebraically using your formula. Show all work.

Answer #1

An archaeologist finds some ancient jewelry made from bone. The
jewelry has a carbon mass of 468 g (HINT: Assume all the carbon is
12C and determine the number of atoms) and careful measurements
show that the remaining 14C has a current decay rate of 12
decays/s. Determine the age of the bone (and presumably the
jewelry). Remember, the ratio of 14C to 12C when the animal died
was 1.3×10-12 & the half-life of 14C is 5730 y. age of...

The found jewelry has a carbon mass of 223 g (HINT:
Assume all the carbon is 12C and determine the number of
atoms) and careful measurements show that the remaining
14C has a current decay rate of 18 decays/s. Determine
the age of the bone (and presumably the jewelry). Remember, the
ratio of 14C to 12C when the animal died was
1.3×10-12 & the half-life of 14C is 5730
y.
I have tried this problem multiple times and have gotten...

The ratio of 14C to 12C in living organisms is 1.3 × 10-12. The
fossilized remains of an organism are discovered and the ratio of
14C to 12C in the fossil is measured to be 2.8 × 10-13. How long
ago, in years was the organism alive? (The half life of 14C is
5,730 years.)
If you answer could you please show all steps on how to find the
answer?
Thank you so much for your time and help!

Q1. Carbon-14 – or 14C – is a radioactive isotope of carbon with
a half-life of 5,730 years. It decays into nitrogen-14 – or 14N – ,
which is a stable isotope of nitrogen.
(a) Which of the three nuclear decay processes describes the decay?
Explain. (Hint: You can get the atomic number of carbon and
nitrogen from a periodic table.)
(b) Write down the equation for the decay.
(c) What is the decay constant for 14C?
All isotopes of...

Carbon 14 is a radioactive isotope of carbon, the most common
isotope of carbon being carbon 12. Carbon 14 is created when cosmic
ray bombardment changes nitrogen 14 to carbon 14 in the upper
atmosphere. The resulting carbon 14 combines with atmospheric
oxygen to form radioactive carbon dioxide, which is incorporated
into plants by photosynthesis. Animals acquire carbon 14 by eating
plants. When an animal or plant dies, it ceases to take on carbon
14, and the amount of isotope...

All living things are radioactive due to the presence of 14 6 C
which undergoes beta decay, emitting an electron. The half-life of
14 6 C is 5730 y. In live specimens, the level of 14 6 C present is
constant. After death, the decay of 14 6 C slowly reduces the
amount of 14 6 C present. Each gram of a live specimen emits 15.3
electrons per minute. An animal bone found at an archaeological
site emits 86 electrons...

Background:
Excavations at Stonehenge uncovered a number of unshed antlers,
antler tines, and animal bones. Carbon-14 dating methods were used
to estimate the ages of the Stonehenge artifacts. Carbon-14 is one
of three carbon isotopes found in Earth’s atmosphere. Carbon-12
makes up 99% of all of the carbon dioxide in the air. Virtually all
of the remaining 1% is composed of carbon-13. By far, the rarest
form of carbon isotope found in the atmosphere is carbon-14.
The ratio of carbon-14...

Cosmic ray bombardment of the atmosphere produces neutrons,
which in turn react with nitrogen to produce radioactive carbon-14.
Radioactive carbon-14 enters all living tissue through carbon
dioxide (via plants). As long as a plant or animal is alive,
carbon-14 is maintained in the organism at a constant level. Once
the organism dies, however, carbon-14 decays exponentially into
carbon-12. By comparing the amount of carbon-14 to the amount of
carbon-12, one can determine approximately how long ago the
organism died. (Willard...

Background:
Excavations at Stonehenge uncovered a number of unshed antlers,
antler tines, and animal bones. Carbon-14 dating methods were used
to estimate the ages of the Stonehenge artifacts. Carbon-14 is one
of three carbon isotopes found in Earth’s atmosphere. Carbon-12
makes up 99% of all of the carbon dioxide in the air. Virtually all
of the remaining 1% is composed of carbon-13. By far, the rarest
form of carbon isotope found in the atmosphere is carbon-14.
The ratio of carbon-14...

please do this step by step and in detail please!!!
extremely stuck on this problem and i just don't get it
help!
30. Radiocarbon Dating.
Carbon 14 is a radioactive isotope of carbon, the most common
isotope of carbon being carbon 12. Carbon 14 is created when cosmic
ray bombardment changes nitrogen 14 to carbon 14 in the upper
atmosphere. The resulting carbon 14 combines with atmospheric
oxygen to form radioactive carbon dioxide, which is incorporated
into plants by photosynthesis....

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