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Is there a formula for the series 1, 8, 18, 32, 50? Sandbh ( talk) 12:30, 5 September 2022 (UTC)
Stephan Schulz, CodeTalker, GalacticShoe, RDBury, Jayron32, Amble: Thanks very much for your contributions.
I agree about the practical quantum effect problems; in periodic table terms it looks like things start becoming moot from, probably at least 119 onwards. I say moot in that 119 is expected to show oxidation states exceeding the +1 normally seen for the alkali metals in group 1. So the approximate recurrence of properties for elements 1 to 118 is expected to start going feral.
The simple formula works up to element 218, which is most elegantly more than adequate.
On H not being a noble gas bear in mind that while H is normally placed above Li in group 1, this does not imply that H is an alkali metal, whereas Li and its heavier congeners certainly are.
The period doubling I'm referring to is the 8, 8, 18, 18 32, 32 occurring in the traditional periodic table from row two onwards:
H He Li Be...B C N O F Ne Na Mg...Al Si P S Cl Ar
The sum of the period lengths is 2+8+8+18+18+32+32 = 118.
OTOH, in philosophy of chemistry there is a fair appreciation of the left step form of periodic table, which has regular periods of length 2, 2, 8, 8, 18, 18, 32, 32. This is achieved by moving He over Be, so that the periods look like this:
H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca
The sum of the period lengths is 2+2+8+8+18+18+32+32 = 120.
While the regularity of period lengths is considered by some to be quite significant, "bangs and stinks" chemists tend to balk at He over Be, since Be is not a noble gas. As well, the left step form scrambles the familiar pattern of metals on the left and nonmetals on the right seen in the traditional periodic table. That said, there are philosophical arguments supporting the left step table, which I won't go into here.
Getting back to H over He, hydrogen is relatively unreactive at room temperature. This is due to the heat of dissociation of the H2 molecule being extremely high, the H-H bond energy being larger than for almost all other single bonds.
Of course H is more reactive than He which is expected to be more reactive than Ne, with neon being thought to be the most noble of the noble gases. Thus H >> He > Ne < Ar < Kr < Xe < Rn. Equally, on the left side of the periodic table, Cs is thought to be the most reactive of the metals rather than Fr. Thus Li < Na < K < Rb < Cs > Fr.
There are other arguments in support of H over He, which I'm not inclined to go into, at least not in this forum.
In terms of precedents:
Sources
Mathematics desk | ||
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< September 4 | << Aug | September | Oct >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Is there a formula for the series 1, 8, 18, 32, 50? Sandbh ( talk) 12:30, 5 September 2022 (UTC)
Stephan Schulz, CodeTalker, GalacticShoe, RDBury, Jayron32, Amble: Thanks very much for your contributions.
I agree about the practical quantum effect problems; in periodic table terms it looks like things start becoming moot from, probably at least 119 onwards. I say moot in that 119 is expected to show oxidation states exceeding the +1 normally seen for the alkali metals in group 1. So the approximate recurrence of properties for elements 1 to 118 is expected to start going feral.
The simple formula works up to element 218, which is most elegantly more than adequate.
On H not being a noble gas bear in mind that while H is normally placed above Li in group 1, this does not imply that H is an alkali metal, whereas Li and its heavier congeners certainly are.
The period doubling I'm referring to is the 8, 8, 18, 18 32, 32 occurring in the traditional periodic table from row two onwards:
H He Li Be...B C N O F Ne Na Mg...Al Si P S Cl Ar
The sum of the period lengths is 2+8+8+18+18+32+32 = 118.
OTOH, in philosophy of chemistry there is a fair appreciation of the left step form of periodic table, which has regular periods of length 2, 2, 8, 8, 18, 18, 32, 32. This is achieved by moving He over Be, so that the periods look like this:
H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca
The sum of the period lengths is 2+2+8+8+18+18+32+32 = 120.
While the regularity of period lengths is considered by some to be quite significant, "bangs and stinks" chemists tend to balk at He over Be, since Be is not a noble gas. As well, the left step form scrambles the familiar pattern of metals on the left and nonmetals on the right seen in the traditional periodic table. That said, there are philosophical arguments supporting the left step table, which I won't go into here.
Getting back to H over He, hydrogen is relatively unreactive at room temperature. This is due to the heat of dissociation of the H2 molecule being extremely high, the H-H bond energy being larger than for almost all other single bonds.
Of course H is more reactive than He which is expected to be more reactive than Ne, with neon being thought to be the most noble of the noble gases. Thus H >> He > Ne < Ar < Kr < Xe < Rn. Equally, on the left side of the periodic table, Cs is thought to be the most reactive of the metals rather than Fr. Thus Li < Na < K < Rb < Cs > Fr.
There are other arguments in support of H over He, which I'm not inclined to go into, at least not in this forum.
In terms of precedents:
Sources