1. 1) "A half-life is the time it trakes for half the mass of a given amount of a radioactive element to decay into its daughter elements"

Is it true that a sample decays "bit by bit"? Why only part of it decays (to daughter elements) and some other part is kept complete untouched (still being the parent isotope)? Won't all parts decay at the same time??

2) "If you were to begin with 10 g of U-238, after 9 billion years, or 2 half-lives, one fourth, or 2.5 g, of the original U-238 would remain. Three fourths would now be the daughter element Pb-206."

The decaying process of U-238 has many intermediate products (like Th-234, Pa-234,etc) before becoming Pb-206. Then is the bolded part true? (25% U-238, 75% Pb-206) How about the intermediate products, would they exist significantly, or would they just exist in an insignificant amount that it can be ignored?

3) "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?)

4) "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?

2.

3. Originally Posted by kingwinner
1) "A half-life is the time it trakes for half the mass of a given amount of a radioactive element to decay into its daughter elements"

Is it true that a sample decays "bit by bit"? Why only part of it decays (to daughter elements) and some other part is kept complete untouched (still being the parent isotope)? Won't all parts decay at the same time??
Each atom in the material will decay seperately. The half-life is the time it takes for half of the atoms to decay. Not all atoms will take the same amount of time to decay, but the half-life will always be the same since you're averaging a large number of atoms.
2) "If you were to begin with 10 g of U-238, after 9 billion years, or 2 half-lives, one fourth, or 2.5 g, of the original U-238 would remain. Three fourths would now be the daughter element Pb-206."

The decaying process of U-238 has many intermediate products (like Th-234, Pa-234,etc) before becoming Pb-206. Then is the bolded part true? (25% U-238, 75% Pb-206) How about the intermediate products, would they exist significantly, or would they just exist in an insignificant amount that it can be ignored?
I think they're assuming that the half-life of the intermediate products is very short.
3) "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?)
The half-life is always the same, but the number of atoms that decays in a given year will change over time. You have to use calculus to find the total amount that decays over a given time.
"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?
Almost all nitrogen is N14, so there would be no way to tell how much of the N14 present was a product of decay and how much of it was already in the sample.

4. Originally Posted by kingwinner
Won't all parts decay at the same time??
I think this is the main question in your post - why doesn't it all just happen at the same time for each particle?
Think of it in terms of probabilities. Say for some substance, any given particle has a 50% chance of decaying each minute it exists. After one minute, half of the particles will have decayed while the other half will have not decayed. After another minute, half of what's left will decay (which totals 75% decayed from the original, and 25% left undecayed).

This substance has a half-life of one minute. Some nuclei are more stable than others, so that % can be higher or lower (and thus, the half-lifes of various substances are also higher or lower).

Sorry if that was a little basic but it seems to be what you were looking for.

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