# Why do nuclei decay so fast and slow?

Why do nuclei like Oganesson (also known as Ununoctium, this is the 118th element on the periodic table) decay in about 5 milliseconds? This is weird that they decay. In comparison, why do elements like uranium take about 200,000 years to decay, or even more? Why do atoms decay at all? Why do elements like Polonium (84th element) take only about 140 days to decay?

• Possible duplicate of Why are synthetic elements unstable? – sammy gerbil Feb 15 '17 at 23:43
• They don't "take time to decay" -- the decay happens instantaneously. The probability of a given atom of a given element decaying in a given amount of time is essentially fixed (as specified by the element's "half life"), but that doesn't say that you couldn't have a given atom decay much sooner or later than it's "half life". – Hot Licks Feb 17 '17 at 4:05
• @sammygerbil no that is not what im asking – science error Feb 17 '17 at 5:00
• As @HotLicks says, the half life is not a fixed decay time. Specifically, the half life is defined as "the period of time after which half the atoms in a sample have probably decayed." Like all random number samples, the accuracy of the half life is proportional to the sample size, with just a handful of atoms your error bars are ridiculously large. – Kaithar Feb 17 '17 at 12:45

In a nutshell, atoms decay because they're unstable and radioactive.

Ununoctium (or Oganesson) has an atomic number of 118. That means that there are 118 protons in the nucleus of one atom of Oganesson, and that isn't including the number of neutrons in the nucleus. We'll look at the most stable isotope of Oganesson, $\mathrm{{}^{294}Og}$. The 294 means that there are 294 nucleons, or a total of 294 protons and neutrons in the nucleus. Now, the largest stable isotope of an element known is $\mathrm{{}^{208}Pb}$, or lead-208.

Beyond that many nucleons, the strong nuclear force begins to have trouble holding all those nucleons together. See, normally, we'd think of the nucleus as impossible because the protons (all having a positive charge) would repel each other, because like charges repel. That's the electromagnetic force. But scientists discovered another force, called the strong nuclear force. The strong nuclear force is many times stronger than the electromagnetic force (there's a reason it's called the strong force) but it only operates over very, very small distances. Beyond those distances, the nucleus starts to fall apart. Oganesson and Uranium atoms are both large enough that the strong force can't hold them together anymore.

So now we know why the atoms are unstable and decay (note that there are more complications to this, but this is the general overview of why). But why the difference in decay time? First, let me address one misconception. Quantum mechanics says that we don't know exactly when an atom will decay, or if it will at all, but for a collection of atoms, we can measure the speed of decay in what's called an element's half-life. It's the time required for the body of atoms to be cut in half.

So, to go back to decay time, it's related (as you might expect) again to the size of the nucleus. Generally, isotopes with an atomic number above 101 have a half-life of under a day, and $\mathrm{{}^{294}Og}$ definitely fits that description. (The one exception here is dubnium-268.) No elements with atomic numbers above 82 have stable isotopes. Uranium's atomic number is 92, so it is radioactive, but decays much more slowly than Oganessson for the simple reason that it is smaller.

Interestingly enough, because of reasons not yet completely understood, there may be a sort of "island" of increased stability around atomic numbers 110 to 114. Oganesson is somewhat close to this island, and it's half-life is longer than some predicted values, lending some credibility to the concept. The idea is that elements with a number of nucleons such that they can be arranged into complete shells within the atomic nucleus have a higher average binding energy per nucleon and can therefore be more stable. You can read more about this here and here.

Hope this helps!

• @fishinear because neutrons in isolation or in small groups are unstable. In nuclei the strong nuclear force between protons and neutrons stabilizes them ... but only up to a point, beyond which adding more neutrons destabilizes rather than stabilizing the nucleus. (On a pedantic note: gravity can also stabilize neutrons, in very large groups known as neutron stars). – nigel222 Feb 16 '17 at 14:42
• @fishinear, spacing them further apart also weakens the strong force; once the distances are big enough, the strong force weakens faster than the electromagnetic force weakens. – ShadSterling Feb 16 '17 at 14:44
• Physics is by far not my strongest field, so I won't even attempt an answer of my own here. But I feel this answer focusses too much on "big nucleus is unstable". Some of the most unstable isotopes are actually isotopes of hydrogen, helium, and lithium. As far as I understood it, it's about imbalance of the nucleus, not necessarily its size. – DevSolar Feb 16 '17 at 16:51
• Yeah, this is pretty much it regarding why heavy nuclei decay. However, there's an aspect you're not seeing, and it's the huge span of timescales of the known decay lifetimes, going from $^7\mathrm H$ at $10^{-23}\:\mathrm s$ to $^{130}\mathrm{Te}$ at $10^{31}\:\mathrm s$, i.e. nuclear physics manages to produce a range of a full fifty orders of magnitude in the dynamics of systems with the same basic constituents and dynamics, which you don't see very often at all. This is partly due to the fact that both the strong and weak nuclear forces come into play, and partly because (cont.) – Emilio Pisanty Feb 16 '17 at 18:51
• decays that involve quantum tunnelling have rates that depend exponentially on the height of the energy barrier they need to "tunnel under". Thus some reasonable changes in the height of that energy barrier produce huge changes in the tunnelling rate. (For more details, though, you'd have to ask someone with stronger nuclear-physics chops than me.) – Emilio Pisanty Feb 16 '17 at 18:52

Indeed, the range of possible decay times is much, much wider than even the range you've given, as I found out myself recently. It's hard to imagine a physical quantity that varies more!

In a big-picture sense, one way to think about this is the following: radioactive decay can be thought of crudely as a form of quantum tunnelling, where the nucleons tunnel out of the metastable nuclear bound state to escape to free space (and in doing so, make the nucleus completely unstable and fly apart). It turns out quantum tunnelling probabilities generically have an exponential dependence: for example, in a simple tunnelling model the tunnelling time goes as

$$\tau \sim e^{\sqrt{\Delta E}}$$

where $\Delta E$ is the height of the energy barrier keeping the particle from escaping.

The effective height of the barrier for nuclear tunnelling is a complicated problem to solve in detail, but the point is that if you were to imagine that it varies by, say, a factor of 1000x between a stable and unstable nucleus, this becomes a difference in decay time that is a factor of $e^{\sqrt{1000}}=10^{13}$. So this exponential dependence magnifies the range of possible values greatly relative to the range of energy barriers, and independent of the microscopic details pretty much guarantees that the range of decay lifetimes will vary widely.

Why do atoms decay at all?

For the same reason that rocks roll downhill. There is a general tendency for things that are at a high energy level to "fall" to a lower energy level.

In terms of atomic nuclei, the lowest energy per nucleon is iron (Fe-56). Energy can be released by fission of elements heavier than iron and fusion of elements lighter than iron.

From this perspective, the question is not "why do atoms decay" but "why is decay not instantaneous?" This is because intermediate states require higher energy. However, quantum systems can "tunnel" through an energy barrier with some probability: https://en.wikipedia.org/wiki/Quantum_tunnelling#Radioactive_decay

So, Polonium-210 isotopes decay at a higher rate than Uranium-238 isotopes because the energy barrier between the initial state and the decay product state is lower.

At low temperatures, fusion does not happen spontaneously at all because the energy barrier is extremely high (though, presumably spontaneous fusion through quantum tunneling can happen, it just has an extremely low probability). In stars, the energy barrier is much lower because the temperature is very high and the nuclei involved have a lot of kinetic energy that allows them to overcome some of the Coulomb forces that repel them (the main cause of the energy barrier).

• It's usually a good idea to include the nucleotide number when dealing with radioactivity. Fe-56 is the most stable, lowest energy-per-nucleon known element/isotope. Fe-59 has a half-life of just 45 days. In fact, there's no radioactive isotope of iron that would be more stable than U-238, which is really barely radioactive at all (which is of course why there's still so much of it left, despite billions of years of decay). – Luaan Feb 16 '17 at 8:47
• @Luaan Added Fe-56. – DepressedDaniel Feb 16 '17 at 18:54

## protected by Qmechanic♦Feb 16 '17 at 7:02

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).