So one can measure the half life of a material just by measuring the amount of the material that one has, and measuring the number of decays that occur during a short amount of time.
For materials with long half lives, measuring decay counts or activity gives a far more accurate determination in shorter time than would waiting for a measurable amount of uranium to decay.
For that reason, I don't think Nij's method of measuring the remaining U238 is used for determining really long half lives. Nij's method also would require the painful step of separating out the remaining U238 from a tiny amount of decay products. I think it would take something on the order of a million years for the U238 to decay enough to allow an accurate measurement using this method.
What is important is that you don't have to wait for half of the uranium to decay to determine the half life.
As i understand, not all lead come from uranium, as they produce naturally throughout the environment. I had someone told me this would make lead unreliable. However, in this case, the half life of uranium will be used since there is no new sources to replenish uranium in the sample. Thus, the remaining of uranium will help determine the age of the sample.
As has been mentioned, the Ur-Pb method are used in situations where the initial presence of lead can be ruled out. I don't sure how just using the remaining uranium would work because we don't directly know the initial amount of uranium. We'd have to infer it from measurements of daughter products.
Mass, radioactivity count, whatever. Just substitute the quantity, the formula still works exactly the same because the pattern is still exactly the same: an exponential decay.
Yes the formulas do work, but some methods for measuring half life are are impractical regardless of what the algebra suggests.
It's very difficult to measure the half life of U238 using the method you describe. After one year of decay 100 grams of U238 would become 99.9999999845 grams of U238 with the decay nuclei still mixed in with the sample. You cannot measure the U238 accurately enough to determine the half-life of U238 even after 1 year.
On the other hand, U238 does emit enough alpha particles (tens of thousands per second per gram) to count over a reasonably short period of time in which the decay rate is constant. For that reason, making an activity measurement is the better approach for determining long half lives.
quote:I'm fairly sure RAZD has slapped this down before too. We don't need to know the original absolute amount; we only need relative amounts i.e. the ratio of uranium to lead, and these can be calculated from the current relative amounts by the simple fact that x uranium atoms turn into exactly y lead atoms; it's a "stoichiometric relationship".
I agree that only the relative amounts are needed for dating purposes. Not disputing that at all.
The paragraph you quoted above was from my addressing a completely different question posed by faith24, namely, whether we could compensate for the situation where lead other than decay products was present simply by measuring the remaining amount of uranium present. My answer is that you cannot compensate in that fashion.