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Any population whether human, animal or atomic nuclei, will with no other complications change proportional to the amount already there. Yielding a very simple differential equation. $$ \frac{dP(t)}{dt} = k\,P(t) $$ where $k$ is a constant with a negative sign for exponential decay and plus sign for exponential increase. i.e. the solution is $$ ...


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If you want to be very nitpicky about it, the decay will not be exponential. The exponential approximation breaks down both at small times and at long times: At small times, perturbation theory dictates that the amplitude of the decay channel will increase linearly with time, which means that the probability of decay is at small times only quadratic, and ...


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A first principle treatment will not yield an exact exponential decay law, see e.g. here.


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Your question drives at the definition of "true randomness", which is a deep question and not altogether resolved. But in short, in modern physics we believe the answer is yes. Indeed there is a whole body of knowledge around Bell's Theorem and the untenability of notions of countefactual reality (the notion that the outcome of a quantum measurement exists ...


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XKCD Radiation chart puts everything in perspective. 1 banana to 1 hour near Fukushima. If you're a beginner in the field, think of contamination(and other radioactive stuff) as the poo and radiation as the stink. You mentioned they weren't wearing suits. The suits are only used for preventing personnel contamination and have little impact of exposure. So ...


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It all depends on the amount of radiation to which one is exposed due to the day-to-day things used. Radium releases alpha particles which have very low penetrating power. Hence we are not in danger of those radiations.


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One has to make clear that the watches we are using now are no longer using radium , because of radiation danger awareness. Radium dials are watch, clock and other instrument dials painted with radioluminescent paint containing radium-226. The 1900s (decade) were the peak of radium dial production, as radiation poisoning was then unknown; subsequently, ...


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By far the most common isotope of Radium is 226Ra, which decays by emitting an alpha particle. Alpha particles have almost no penetrating ability, and in general externally- occurring alpha particles are absorbed by the outer layers of skin which are naturally sloughed off, so no permanent damage occurs. If you swallow it, that's a whole other (very sad) ...


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Humans can tolerate a certain amount of radiation. The watch contributes less radiation to our bodies than the soil. Radium emits x-rays, so yes, they can excite an electron.


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Yes you can compute the total number of nuclei from such a graph. Basically, if you plot # of decays per second on the Y axis, and time on the X axis, then the area under the curve (if your curve ran all the way to infinite time) would be "all the nuclei" since they all decay exactly once. If you have just a short time segment, you can estimate the half ...


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There is a large class of weak decays that can be predicted fairly well from theory (using the notion of weak universality). However, I have in mind the weak decay of heavy leptons and individual hadrons, so that is not quite what you were asking for as it occurs outside the nuclear context. You can tackle the nuclear problem too, but the phase space ...


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In theory it could be done. The problem is that we're dealing with hundreds of entangled nucleons. A particle can be modeled as a wave in three-dimensional space. Two particles that aren't entangled can be modeled as two waves. But if they are entangled, you have to use one wave in six-dimensional space. In order to model an atomic nucleus, you'd need ...


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It is a prompt (immediate) reaction, and is more usually written something like N14(n,p)C14 to indicate that. It is far from the only such reaction. EDIT - To quantify my statement that there are many similar reactions, I went to the Evaluated Nuclear Data Files site hosted at Brookhaven (ENDF), entered 'n,p' for the reaction, 'sig' for the desired ...


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In regards to a single element, this actually happened. Natural Bismut is about 100% 209Bi, which shows no obvious indication of being radioactive. But it turned out that all existing bismuth is radioactive. The isotope 209 had been suspected to be unstable before, but that was experimentally verified as recently as 2003, finding a half life of 1.9×1019 ...


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Most atoms have an ionization energy of a few tens of electron volts. Beta decay electrons typically have a range of energies, with the mean and maximum energies typically a few million electron volts; the probability that the electron energy is small enough to be captured is pretty small. In addition, the daughter atom cannot capture the decay electron ...


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If protons decay, then what you say is true: all atomic nuclei are indeed unstable, and a so-called "stable" nucleus simply has too long a half-life for its decay to be observed. The most tightly bound nucleus is $^{62}$Ni, with a binding energy per nucleon of 8.79 MeV [source], which is less than 1% of the mass of a nucleon. On the other hand, the decay of ...


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We are never 100% certain of anything. The scientific method falsifies wrong theories, but it does not verify those we colloquially call "correct" or "true" If we tomorrow detect a normal oxygen atom decaying, we'll have to devise new theories to explain it. But we don't expect the things we call stable to ever decay (that's why they're called stable). We ...


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Yes, the atom (along with the surrounding material) may have a lasting electron deficit after the beta particle emission because harvesting this surplus charge is how betavoltaics work. Beta particles are more penetrating than charged nuclei like alpha particles, and because of that I believe they are better at carrying the charge away. The exact reasons ...



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