# How are billion-year half-lives approximated? [duplicate]

Our life-time is negligible, compared to that of unstable nuclei with half-lives of billions of years.

How, then, are these half-lives estimated, if you may never even witness a decay. It's like estimating the probability of a popcorn kernel popping, after one of the 200 in a pan has popped.

Would it be done over, say, a decade, with a massive amount of the source constantly monitored by a gygameter? Wouldn't the data still be inconclusive?

Is it estimated other ways, such as by examining the relationship between the composition of an atom and its half-life, to extrapolate larger half-lives? Comparing the quantities of the nucleuses isotopes found in nature, to extrapolate?

-- How on earth could scientists know that Lead-204 has a half-life 10,000,000 time longer than the age of the universe ~14,000,000,000 so: 140,000,000,000,000,000 years.

• @Countto10 That's not a duplicate... "Logically, shouldn't it take 2,865 years for the quarter to decay, rather than 5,730?" Does that read similarly to anything I've asked? – Tobi Mar 2 '17 at 13:38
• @Tobi It kind of is though. But it isn't clearly so -- it doesn't use the exact same words you do, but the answer to that other question is the same answer to yours. – tpg2114 Mar 2 '17 at 13:41
• And your question ultimately boils down to "How does half-life work" and the answer is the same. There is a whole lot of atoms in a small sample of material, and by observing them and counting how many undergo changes, you can figure out the half-life. If there is 10^22 atoms in a sample, you don't need to wait 10^18 years to see a change. – tpg2114 Mar 2 '17 at 13:44
• – Jon Custer Mar 2 '17 at 13:51
• Move on, as in? I successfully got the answer to my question, even with the pedantry/instigative nature, typical of stackexchange forums – Tobi Mar 2 '17 at 14:02

Because there are a lot of atoms. Lets take the example of lead 204. If we take 1 Mol, which is 204g we have $6×10^{23}$ atoms. You say half-life is $140×10^{15}$years which is around $4×10^{24}$ seconds. So in a crude estimation you still should have around 1 decay every ten seconds. In order to find this, you look for the outgoing radiation, not for the decay product.