I think the “mile wide” statement was a thought experiment to try and show that quantum behavior cannot really exist. IOW if a nucleus was 1 mile wide, the electron cloud would be around 10,000 miles wide, and everybody knows that large objects moving over long distances have measurable characteristics and behave in a predictable, familiar fashion. Thus if the electrons orbiting a mile-wide nucleus move in continuous trajectories at finite measurable speeds, then they must likewise do so around the actual quantum nucleus.
In fact the behavior at the quantum level is totally different and does not follow normal intuition. It is not possible to make a mile-wide nucleus, nor magnify the quantum nucleus and view it with equivalent resolution. From a quantum standpoint, electrons are point particles and have no physical size, or at least no measurable size. Making a zero-size particle a million times bigger would still be zero size.
Likewise electron tunneling is considered to work at infinite speed so if you make the tunneling barrier a mile wide and the electron the size of a basketball it would appear to teleport over that distance in zero time. This cannot really happen at the macro level but that seeming implausibility does not mean it doesn’t happen at the quantum level.
There is no such thing as a “macro level” absolutely distinguishable from the quantum level. Quantum mechanics applies at all levels. It might be very, very difficult to keep an electron in a mile-wide orbital, but it probably actually happens in deep intergalactic space.
And while H[sup]+[/sup], i.e., a bare proton, does have interesting chemical properties, it has those properties mostly by virtue of the potential to have electrons in particular configurations in its vicinity.
Because in VERY empty space it may be possible to have isolated nuclei, with nothing nearby for miles.
While it is true in principle that an electron belonging to a nucleus or molecule in your body has the possibility of being detected out at Jupiter’s orbit, the fact is that that electron will feel forces from numerous other nuclei much more strongly than it will feel forces from its parent in your body, and it will effectively be lost. This happens over microscopic distances in solids and liquids and normal gases (the places where we live). But in deep space, perhaps in the “bubbles” between strings of galactic clusters, nuclei may be very isolated.
Because as Z increases, there is ever more axis to higher level orbitals (s, then p, then d, then presumably others). The periods (rows) become wider and wider. Atoms become smaller as you move to the right in a period.
I’m just guessing that somewhere around Z = one million, that increased “tightness” of an individual orbital caused by higher positive charge in the nucleus will more than offset the fluffiness of additional electrons.
At any rate, even if we don’t see atoms getting smaller with higher Z, they don’t get a lot larger, either.
Even if one imagines a “YUGE” nucleus the size of a basketball, I don’t think current understanding of atoms says that the electrons have to be outside of the nucleus, and I think calculation of the (90%ile) orbits would be comparable to ordinary atoms.
I don’t understand this. The probability of finding a bound electron far from the nucleus drops off quickly. This calculator shows the probability of finding a bound electron far away from the nucleus quickly becomes essentially zero: Hydrogen Ground State Properties
If you mean there is practically zero but mathematically non-zero expressible probability, this has no practical meaning since math can easily express things which far exceed the material universe. There are only 8x10^184 Planck volumes in the universe and Planck time is 5.3x10^-44 sec, but it is trivial to vastly exceed these and all combinations of space/time values. This means a tiny but non-zero mathematical probability expression has no necessary practical meaning to the discussion at hand:
Z is the number of protons in the nucleus. How could you have a nucleus with a million protons since the strong force cannot hold together a nucleus with more than about 126 protons?
This site seems to imply there is a maximum size to the nucleus and hence the periodic table, unless nuclei are made of strange matter.
IIRC from my undergraduate physics days the liquid drop model or semi empirical mass formula also limits the binding energy of a nucleus, so theoretically this would put an upper limit on the size of the nucleus.
Re. drip lines: this is the limit on how unbalanced a nucleus can be in its proton/neutron raitio. If I’m understanding the article correctly, it’s saying that far enough up the table of nuclei the two lines intersect- that is, beyond that a nucleus would be unstable against both beta decay and positron emission.