Radiometric Dating & the stability of isotopes

[ST88]

I have always wondered about this. I understand that the workings of such radiometric clocks are based on probability theory of how long it would take a given isotope to decay into a lighter element. I have seen it described as an hourglass, where you don't know which particle of sand will fall through the throat of the glass at any given time, but you know it will be one of them.

My question is, how come the particles of the isotope all don't go off at once, and how come we would never expect that this might happen? If the conditions are right for decay, why would we accept that the entire set of atoms of this particular element would look at each other from time to time and say, "OK, who's next?"

[ENIGMA]

I have always wondered about this. I understand that the workings of such radiometric clocks are based on probability theory of how long it would take a given isotope to decay into a lighter element. I have seen it described as an hourglass, where you don't know which particle of sand will fall through the throat of the glass at any given time, but you know it will be one of them.

My question is, how come the particles of the isotope all don't go off at once, and how come we would never expect that this might happen? If the conditions are right for decay, why would we accept that the entire set of atoms of this particular element would look at each other from time to time and say, "OK, who's next?"

From my understanding of it, it is a purely probabilistic decay (something about quantum effects comes to mind, but I'm blanking afterwards). Each particle has an independant probability of decaying such that at any given time it has a 50% chance of decaying within the period of time specified by its half-life. Since this is perpetually the case, any residual amounts of the isotope which have not decayed will be equally likely to decay in the next interval.

The reason that the individual probabilistic decays work out to be such an accurate proportion is the statistical law of large numbers which shows that the larger a random sample is, the more likely it is to tend toward the mean of a population. Seeing as any macroscopic sample will contain many billions of particles, it should yield a fairly accurate impression of the mean of the source of the sample, and thus the overall decay.

[mrmufin]

My question is, how come the particles of the isotope all don't go off at once, and how come we would never expect that this might happen? If the conditions are right for decay, why would we accept that the entire set of atoms of this particular element would look at each other from time to time and say, "OK, who's next?"

My understanding of decay is pretty much consistent with ENIGMA's; that is, the larger the sample size, the more accurate the decay rate can be determined. Strictly speaking, I don't think that anything necessarily prevents all of a radiocative sample from decaying at once, only that that would be very highly unlikely. As to whether or not "the conditions are right for decay," it is also my understanding that decay is not contingent upon any external conditions or forces.

Regards,
mrmufin