Absolute Age: Radiometric Dating(2)

[kingwinner]

1) "By comparing the amounts of U-238 and Pb-206 in rock samples, the age of the sample can be determined. Scientists know that from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced by decay. The U:Pb ratio can be used only when the sample has not gained or lost lead or uranium since its formation."

 

Does anyone know where the "1/7600" comes from? I don't know how they can get the rate of decay per year, wouldn't the rate of decay be different each year, because of the concept of half-life (1/2 of the original amount for a certain time, right?)

 

 

2) "The half-life of C-14 is 5,730 years. To establish the age of a small amount of organic material, scientists first determine the proportion of C-14 to C-12 in the sample. They then compare that proportion with the proportion of C-14 to C-12 known to exist in a living organism."

 

Why should we determine the proportion of C-14 to C-12 in the sample? Can we just determine the proportion of C-14 (parent isotope) to N-14 (its daughter isotope) instead, like the U-238:Pb-206 in question 1?

 

Thank you in advance!

[Turtle]

1) "By comparing the amounts of U-238 and Pb-206 in rock samples, the age of the sample can be determined. Scientists know that from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced by decay. The U:Pb ratio can be used only when the sample has not gained or lost lead or uranium since its formation."

 

Does anyone know where the "1/7600" comes from? I don't know how they can get the rate of decay per year, wouldn't the rate of decay be different each year, because of the concept of half-life (1/2 of the original amount for a certain time, right?)

 

Thank you in advance!

 

---The rate of decay is constant & acting on a changing amount. If you decay 1/2 of a radioactive element in given sample in say a year, then the next year's decay is affecting 1/2 of half-as-much as you started with, so at the end of the second year you have decayed 1/2 + 1/4 = 3/4 of the total radioactive element in the original sample.

___The time interval of 'one year' is arbitrary however. If you take your time interval as 6 months (1/2 year), then you count 1/2 + 1/4 + 1/8 +1/16 = 15/16. I don't know what what time interval they use or how they determine it.

___I don't know about the Carbon; I hope I haven't confused the issue or mistated the case for you King. Fortunately if I have, someone here surely will set it straight.

___Keep on rockin'!:cup:

[CraigD]

Good questions!

1) "By comparing the amounts of U-238 and Pb-206 in rock samples, the age of the sample can be determined. Scientists know that from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced by decay. The U:Pb ratio can be used only when the sample has not gained or lost lead or uranium since its formation."

 

Does anyone know where the "1/7600" comes from? I don't know how they can get the rate of decay per year …

The 1/7600 should come from a trivial algebraic derivation of the 1-year decay rate ® from the half-life of U-238 (4.468*10^9, according to the Wikipedia article “Uranium”:

R^4.468e9=.5

R=b^(Logb(.5)/(4.468*10^9)) = ~.999999999844864105 = ~ 1 –1/6446

 

Not quite the quoted 1/7600 – I suspect the discrepancy is due to an averaging adjustment, pertaining to the 2nd part of your question …

… wouldn't the rate of decay be different each year, because of the concept of half-life (1/2 of the original amount for a certain time, right?)

Yes. For rocks less than a billion (10^9) years old, the decay would have a small (less than 20%) impact on the original U-238 mass, but for longer periods (the oldest rocks are thought to be 4*10^9 years old), the crude calculation you quote wouldn’t be appropriate.

 

I think the source you’re quoting is “dumbed down” for an audience assumed be ignorant of “higher math” such as exponentiation, making it potentially confusing for better informed readers. In general, I think Science would be better understood is writers were more careful in their explanations, and avoided such crude “dumbing down”.

[CraigD]

2) "The half-life of C-14 is 5,730 years. To establish the age of a small amount of organic material, scientists first determine the proportion of C-14 to C-12 in the sample. They then compare that proportion with the proportion of C-14 to C-12 known to exist in a living organism."

 

Why should we determine the proportion of C-14 to C-12 in the sample? Can we just determine the proportion of C-14 (parent isotope) to N-14 (its daughter isotope) instead, like the U-238:Pb-206 in question 1?

I’m not a trained biochemist, but I think that N-14, being relatively non-reactive and a gas at room temperature and pressure, and the primary (99%+ occurring) isotope of nitrogen, is taken into and excreted from a living creatures cells in such great quantities (about 20 kg/day for a human) that the tiny amount produced by C-14 decay is undetectable.

[kingwinner]

Good questions!The 1/7600 should come from a trivial algebraic derivation of the 1-year decay rate ® from the half-life of U-238 (4.468*10^9, according to the Wikipedia article “Uranium”:

R^4.468e9=.5

R=b^(Logb(.5)/(4.468*10^9)) = ~.999999999844864105 = ~ 1 –1/6446

 

Not quite the quoted 1/7600 – I suspect the discrepancy is due to an averaging adjustment, pertaining to the 2nd part of your question …Yes. For rocks less than a billion (10^9) years old, the decay would have a small (less than 20%) impact on the original U-238 mass, but for longer periods (the oldest rocks are thought to be 4*10^9 years old), the crude calculation you quote wouldn’t be appropriate.

 

I think the source you’re quoting is “dumbed down” for an audience assumed be ignorant of “higher math” such as exponentiation, making it potentially confusing for better informed readers. In general, I think Science would be better understood is writers were more careful in their explanations, and avoided such crude “dumbing down”.

1) My quote says that "from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced ". How is this possible? :cup: The amount of Pb-206 produced each year shouldn't be constant (half-life...), right?

[kingwinner]

I’m not a trained biochemist, but I think that N-14, being relatively non-reactive and a gas at room temperature and pressure, and the primary (99%+ occurring) isotope of nitrogen, is taken into and excreted from a living creatures cells in such great quantities (about 20 kg/day for a human) that the tiny amount produced by C-14 decay is undetectable.

2) My text book says "Radioactive isotopes function as natural clocks. Scientists measure the concentrations of the original radioactive isotope and the newly created isotopes. They then compare the proportions of the original and new isotopes to determine the absolute age of the rock."

So is this the general way of calculating the absolute age of a sample using radiometric dating, while C-14 dating is kind of like an exception? (because they don't compare the proportions of parent isotope to daughter isotope...they compare C-14 and C-12 instead, and C-12 is not a daughter isotope of C-14)

[CraigD]

1) My quote says that "from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced ". How is this possible? :cup: The amount of Pb-206 produced each year shouldn't be constant (half-life...), right?

Right. The quote is oversimplifying the Math and Science so much that it is inaccurate.

[CraigD]

2) My text book says "Radioactive isotopes function as natural clocks. Scientists measure the concentrations of the original radioactive isotope and the newly created isotopes. They then compare the proportions of the original and new isotopes to determine the absolute age of the rock."

So is this the general way of calculating the absolute age of a sample using radiometric dating, while C-14 dating is kind of like an exception? (because they don't compare the proportions of parent isotope to daughter isotope...they compare C-14 and C-12 instead, and C-12 is not a daughter isotope of C-14)

Yes.

 

Radiocarbon dating circumvents our inability to measure N-14 due to C-14 decay by assuming that living tissue starts a known ratio of C-14 to carbon’s major, stable isotope, C-12, allowing us to consider just this ratio in the sample.

 

Note that this introduces many possible source of error – if the air, water, or food sources had an unusual amount of C-14 when the sample last metabolized it, radiocarbon dating using the standard assumption will give a very incorrect date. The low radioactivity of aquatic plants is such a complicating factor (makes samples appear older than they actually are). The increased atmospheric radiation due to 20th century nuclear weapon testing will, many years in the future, complicate the dating of samples from this period. (will make samples appear younger than they actually are). Accurate radiocarbon dating requires careful analysis of such factors using many different scientific techniques.

[kingwinner]

Thanks a lot for explaining! You're so nice!