eli5 : is there a limit to the number of trans-uranium elements that can be in the periodic table?

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Someone told me that there is a limit to the number of trans uranium elements that can be in the periodic table. His reasoning was that when the number of electrons for an element gets big enough, the electrons in the outer shell will be so far out that they will have to travel faster than the speed of light to orbit the nucleus. Could he be right?

In: 22

That’s not a great argument, because electrons don’t have well-defined locations and speeds, and they don’t “orbit” their nuclei in a way that you can calculate an orbital velocity.

First, electrons don’t really orbit the nucleus like that. They don’t travel around the nucleus, they “orbit” in stationary standing waves called orbitals.

Second, even if electrons did move in circular orbits, that wouldn’t have any effect on whether or not the element could exist. Elements are defined based on the number of protons in the nucleus, not on how many if any electrons are orbiting that nucleus.

Finally, yes, there is a “limit” to the number of transuranic elements that can exist, but it’s not due to electrons. It’s due to the nucleus itself being unstable. There’s an arbitrary minimum lifetime of 10^-14 seconds before decay that an element must live to be considered to actually exist as an element by scientists. Above a certain size, nuclei just aren’t stable enough to live that long.

That’s a pretty terrible argument since elements are defined by the number of protons in the nucleus, and the number of orbital electrons doesn’t have anything to do with that. If we could make a “stable” nucleus (in quotes because we’d probably be talking about a lifetime of a fraction of a nanosecond) big enough to have that happen, we’d just note that it can only exist as an ion and not in the elemental state of neutral charge.

Since that would be the smallest element with that property, you wouldn’t have made the last element, but made the first of an entirely new group of permanent ions and be collecting your Nobel Prize in short order.

There are known challenges to creating extremely heavy elements, and none have been observed occurring naturally. We’ve really struggled to keep the higher ones we make now stable, and prevent them from decaying down to a smaller element.

But there’s also no known reason element 200, 1,000, or 1,000,000 can’t exist. We just haven’t developed a way to create them and find out if they’re stable yet.

https://en.m.wikipedia.org/wiki/Island_of_stability

There is a lot of unknown physics about very heavy elements. We don’t really know where it stops or have a solid way of predicting the patterns of stability.

The consensus theory right now says that elements go on forever, with islands of stability that get increasingly rare as mass goes up.

I find your friend’s comment about electrons dubious because the stability of an isotope generally doesn’t have anything to do with its electron shell. Ions form readily and are stable and electrons do not contribute to nuclear interactions between protons and neutrons.

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Less salient, I also find his take about impossible speed dubious. Anything, including an electron, can gain arbitrary amounts of momentum without exceeding the speed of light – that’s the whole point of Special Relativity.