I guess you can think of a lot of dice. They might be identical but you wouldn't expect to get the same number when you throw all of them, because when you do, you are assigning to each one a different initial condition. I guess it's similar with atoms. Although each decay is a random and spontaneous phenomenon, it is a quantum mechanical process ruled by probabilities because the uncertainty principle doesn't allow you to know the exact initial (energy) state of each individual atom (it's non-deterministic). Some atoms might be in an initial energy state that favors a quick tunneling to a lower state and decay, but others might not and might take longer to stabilize, therefore you need to treat them statistically as a sample or population with a certain probability 'lamda' of decaying. Specifically, you need to treat them under the Poisson distribution, since it expresses the probability of a given number of events occurring in a fixed interval of time, if these events occur with a known constant mean rate (lamda) and independently of the time since the last event.

Thank you very much for you answer, dear Fulvio.

Many thanks to Fulvio-Farina-Arbocco for his answer and i want to add the following:

Unlike classical physics, in which a particle can not overcome a potential greater than its kinetic energy, a quantum particle can tunnel through the potential barrier in a nucleus. Quantum mechanically speaking it is impossible to predict the decay of a single atom. In fact, the time evolution of such system is described by a wave packet that is a solution of the Schrödinger equation with the potential included. The moving wave can strikes the potential barrier and a part of the packet tunnels through and there is a chance for some transmission and therefore the occurrence of a decay.

Dear prof.Askari

Thanks a lot for your answer to my question, but where is this wave of pocket coming from?

My Dear Mohammed kooti

Radioactive or unstable nuclei emit radiation in the form of energy and particles in a process known as radioactive decay. The length of time required for a nucleus to decay varies from isotopes to isotopes. One measure of the length of time needed is the half-life. And that all isotopes contain a fixed number of protons, but they differ in the number of neutrons, and the ratio between N/Z determines the type of radiation and according to the rules of selection

Neutrons and protons, like electrons in the atoms and molecules, behave randomly, although following probalistic rules, as it is the case for all processes at atomic and nuclear scale, that are described by the probalistic laws of quantum physics.

Thus the radioactive transformation occurs randomly. Even if they have the same composition and energy, two nuclei of the same radioactive nuclide are never in the same internal configuration.

Thank you very much for your answer prof. Tandeur.

Radioactive decay is a random phenomenon. Hence all atoms of a radioactive element do not decay simultaneously but instead only a few atoms on random basis decay depending on half life which is a controlling factor.

My Dear Mohammed kooti

Radioactive or unstable nuclei emit radiation in the form of energy and particles in a process known as radioactive decay. The length of time required for a nucleus to decay varies from isotopes to isotopes. One measure of the length of time needed is the half-life. And that all isotopes contain a fixed number of protons, but they differ in the number of neutrons, and the ratio between N/Z determines the type of radiation and according to the rules of selection

Thank you very much prof.Garg for your interesting answer to my question.

Dear Ali

I am talking about isotopes which have the same number of protons and neutrons.

How do you know they're identical. Are each of the radioactive atoms in the sample all of the same age, born at the same point in spacetime? One could never know; there's no "born on" date we can measure at the subatomic level. (But this is facetiousness.) Fermions have different states, too, such as spin etc. And when you measure that, you change it... so to determine true identicality at the quantum level, the measurement process would cause non-identicality.

The easiest answer is that decay, like any quantum mechanical process, is a wave function, and like most things in quantum mechanics we need the Schrodinger equation for that. And so the model we have for predicting radioactive decay gives a probability, and thus there will be a distribution of half-lives across "identical" radioactive atoms in a large sample. At the individual atomic level, no atom will be found to have the exact same half-life we measure for a whole sample.

Here is an interesting video: https://www.youtube.com/watch?v=6e9CE7neVrc&list=PLX2gX-ftPVXXt6Ix6JWYCiv5yJYV7DO2K&index=92

You asked

"If all atoms in a radioactive isotope are identical, why don't they all decay simultaneously?"

All the atoms in a given radioactive isotope, say Ra-226, have the same number of protons and neutrons. Ra-226 nucleus has 88 protons and 138 neutrons. All Ra-226 atoms are identical in the number of protons and neutrons.

There are hypothesized internal structures of atomic nuclei. All hypotheses include nuclear structures and energy states. The structures and states include include forces (Coulomb, strong, weak, ...) and exchange particles (gluons ...). All of these provide endless fun for theorists and high-energy physicists.

All Ra-226 nuclei are identical in the number of protons and neutrons, but the indentiy ends there, Nevertheless, we know a lot of descriptive information about Ra-226 that we simply relate to that combination of 88 + 138. We cannot tell you why it has a particular half-life, but we can get close. For a given atom, we cannot tell you when.

“If all atoms in a radioactive isotope are identical, why don't they all decay simultaneously?”

Such passages as

“…Neutrons and protons, like electrons in the atoms and molecules, behave randomly, although following probalistic rules, as it is the case for all processes at atomic and nuclear scale, that are described by the probalistic laws of quantum physics. Thus the radioactive transformation occurs randomly. Even if they have the same composition and energy, two nuclei of the same radioactive nuclide are never in the same internal configuration.….”

- or

“…. I guess it's similar with atoms. Although each decay is a random and spontaneous phenomenon, it is a quantum mechanical process ruled by probabilities because the uncertainty principle doesn't allow you to know the exact initial (energy) state of each individual atom (it's non-deterministic). …”

- really aren’t some clear enough answers, say, all what is in the quotes happens in stable nuclei and stable atoms’ ground states also;

- and, besides, besides unstable nuclei and unstable stable atoms’ excited electron shells’ states there exist unstable particles, which also decay somehow, including, say, heavy leptons, which, as now physics states, aren’t composed from some “smaller” particles.

While yeah – all items above are quantum mechanical object, while QM rather essentially is based on the postulate that one type particles, and even one type atoms, are absolutely identical – what really follows from that all experimentally measured parameters of the items above, and one type compositions of the items, are identical, and, moreover, at interactions of particles; including, say, when particles compose atoms’ shells and atoms’ nuclei, the “exchange forces/interactions” act, which are as they are only provided that the postulate above is true.

Real answer to the thread question – including why in QM – and in the reality - the “identity postulate” above really exists/acts can be, and is, given only in the Shevchenko-Tokarevsky’s informational physical model , two main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics and

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics,

- which [the model] is based on the really philosophical 2007 SS&VT “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- where it is rigorously proven that there exist nothing else than some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set.

So there is nothing surprising in the identity of the items above – that are simply identical copies of some the same “texts”; what is quite natural in the absolutely fundamental phenomenon “Information”, say, this text can have any number of completely identical copies,

- while one type particles and atoms are specific “texts” – that are close-loop algorithms that run basing on “hardware” of the ultimate base of Matter – the primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4+1]4D dense lattice, which is placed in the Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),

- which [the algorithms] always constantly cyclically run.

At that if some algorithm has some defect, it can with some probability break on some its tick; and that really happens, correspondingly exponentially in time, and not simultaneously.

Cheers

They are not indeed "identical' ...........

They are not indeed "identical' ...........