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?

I have no idea about the uranium but I'm familiar with the 14C method. 14N is the regular nitrogen isotope that is rather abundant in organisms as a essential element in proteins. The tiny spores of nitrogen from decaying 14C is not discernible from that mass.

For a good sampling the 12C is also compared with the 13C as several fractination processes during the biological processes do change all those ratios. So the d13C of the sample does say something about those processes since it is stable and does not change over time and this is used to estimate the original 14C contant, since the fractination of 14C is double that of 13C. This is important since there are two different photo synthesis assimilation processes, C3 and C4, with considerable difference in 13C and 14C fractination.

I have no idea about the uranium but I'm familiar with the 14C method. 14N is the regular nitrogen isotope that is rather abundant in organisms as a essential element in proteins. The tiny spores of nitrogen from decaying 14C is not discernible from that mass.

For a good sampling the 12C is also compared with the 13C as several fractination processes during the biological processes do change all those ratios. So the d13C of the sample does say something about those processes since it is stable and does not change over time and this is used to estimate the original 14C contant, since the fractination of 14C is double that of 13C. This is important since there are two different photo synthesis assimilation processes, C3 and C4, with considerable difference in 13C and 14C fractination.

2) Then why should we determine the proportion of C-14 to C-12 in the sample? If we just determine the proportion of C-14 (parent isotope) to N-14 (its daughter isotope) instead, i.e. comparing the ratio of the parent and its daughter isotope in a sample, would it still work? (in estimating the absolute age)

1) The 1/7600 of 1g is the product of a defined 1,000,000 g U238. You are correct that if we stay with that original mass the proportion of Pb generated will be lower each year, but the definition says from a starting mass of 1,000,000g.
2) The nitrogen is a gas: up, up and away.

1) The 1/7600 of 1g is the product of a defined 1,000,000 g U238. You are correct that if we stay with that original mass the proportion of Pb generated will be lower each year, but the definition says from a starting mass of 1,000,000g.
2) The nitrogen is a gas: up, up and away.
1) But it says "from a million grams of U-238, 1/7600 g of Pb-206 per year will be produced ". How is this possible? :bugeye: The amount of Pb-206 produced each year shouldn't be constant (half-life...), right?

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)

Well 14C is not all that different from other radiogenic techniques. The ratio of 14C in the atmosphere is (incorrectly) assumed to be constant thougout the time and during life time the constant cycle of carbon between life organisms and the atmosphere also keeps that ratio constant albeit slightly different due to fractinations.

So as soon as the organism dies the exchange of carbon stops and the 14C decay clock starts ticking, reducing the ratio of 14C to 12C