How radioactive dating works? Often in geology & archaeology we listen that they calculated the age of things (bones, pots) using radio active dating.
Radioactive dating works using half life of unstable isotopes. And what geologists/archaeologists do is use the fraction of remaining isotopes.
But this makes no sense to me. I mean should not it be that those isotopes start decaying right after they were created (probably inside star cores or explosions ) instead of when that pot was created?
 A: When I first learned about radio-isotope dating, I was puzzled in just the same way.  $^{14}C$ dating for example: why is the behaviour of the carbon atoms affected by whether something is alive or not?  The answer is that to be useful there must be some process that in a sense resets the clock.  The maths may be similar from case to case but this clock resetting varies from case to case.
Radiocarbon dating
In this case, the extra factor is that, despite decaying, the proportion of $^{14}C$ in the atmosphere is approximately constant.  This is due to the reaction of cosmic rays with nitrogen in the upper atmosphere.  Living things share this (approximately) fixed proportion since they are always exchanging carbon with the atmosphere.  However, when they die this stops.  The $^{14}C$ inside them continues to decay but it is no longer replenished.
Potassium Argon dating
This is very different.  Potassium naturally contains some $^{40}K$ some of which decays into $^{40}Ar$.  The extra factor this time is that argon is a noble gas.  So, it does not chemically combine with the other elements around it.  If it is in a solid rock then it is trapped but if the rock melts then it can bubble out and escape.  So, melting of the rock resets the clock.  Measuring the argon can tell you how long since the rock was molten.
A: Radiometric dating measures the time since an object became a "closed system", which means it stopped exchanging isotopes with the external environment. For minerals and crystals this is usually when the mineral or crystal was formed from molten rock.
Radiometric dating methods depend on knowing the original proportion of parent atoms to decay product atoms in the object. A measurement of the current proportions, together with the half-life of the isotope, can then be used to estimate the time since the rock was formed. Sometimes several independent radiometric dating estimates can be made based on different decay chains, and can then be compared for consistency.
The age of organic remains (such as bones, shells or wood) can be estimated using radiocarbon dating. The origin point here, when the organic remains became a closed system, is when the animal or plant died.
Radiocarbon dating can be used to date artefacts made from organic material, such as wood, papyrus or cotton. What is being estimated is when the tree was felled, for example, rather than when the object was actually made, but these points are assumed to be close together in time. As far as I know there is no version of radiometric dating that can estimate when a pot was made, unless it contains some organic material.
A: You can't just use anything. You need to pick something where initial ratios are known. For example, a crystal formation that has the tendency to reject the decay product during formation, then you compare the ratio of decaying product to decayed product.
Zircon is the quintessential example. During formation, it has the tendency to incorporate uranium but reject lead, which uranium decays into, from its lattice.
And the fact it is picky with materials means you probably aren't able to radioactive dating directly on the pot, but are using it on the rock the pot is buried in. So although you are using radioactive dating to try and estimate the the age of the pot, you aren't using it on the pot.
