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?

For question 1, to clarify what I meant...I mean won't all the atoms decay all together at the same rate? Is it just happening that only some atoms decay while others are completely untouched??

For question 1, to clarify what I meant...I mean won't all the atoms decay all together at the same rate? Is it just happening that only some atoms decay while others are completely untouched??

No, they do not all decay at once although it is the same rate. It's a statistical thing and has been proven quite accurate by experimentation. The atoms are unstable and break down at a precise and predictable rate.

For an example, consider a large number of humans, say 10 million. We know that all humans die - but not at the same time or same age. But for a given day, you could accurately predict how many will die (assuming the same conditions for all) based on gathering data and computing the statistics. You could even carry it farther and predict how many in the age group of 45-50 will die on any one day.

Realize that this is not the same as atomic physics but the same principles apply for the purpose of the example.

In answer to question 2:
If you look at the decay chain of U238, the half-lives of daughter products are insignificantly short compared to the half-life of U238. Daughter product half lives range from microseconds to a couple of hundred thousand years- the cumulative half-life of all the daughter products is approximately 300,000 years (compared to ~4.5 billion years for U238). Because the daughter products decay so much more quickly than the U238, they would make up a small, but insignificant, amount of the sample.