[seqfan] Re: Another chemistry related sequence?
jvospost3 at gmail.com
Thu Sep 3 16:03:25 CEST 2009
The two greatest unknowns at the upper fringes of the Periodic table
are: (1) The island of stability, a term from nuclear physics, first
proposed by Glenn T. Seaborg, that describes the possibility of
elements with particularly stable "magic numbers" of protons and
neutrons. This would allow certain isotopes of some transuranic
elements to be far more stable than others; that is, decay much more
slowly. A filled shell would have "magic numbers" of neutrons and
protons. One possible magic number of neutrons is 184, and some
possible matching proton numbers are 114, 120 and 126 — which would
mean that the most stable possible isotopes would be ununquadium-298,
unbinilium-304 and unbihexium-310. Of particular note is Ubh-310,
which would be "doubly magic" (both its proton number of 126 and
neutron number of 184 are thought to be magic) and thus the most
likely to have a very long half-life. (The next lighter doubly-magic
nucleus is lead-208, the heaviest stable nucleus and most stable heavy
metal.) None of these superheavy isotopes has yet been produced, but
isotopes of elements in the range between 110 through 114 have been
found to decay more slowly than isotopes of nuclei nearby in the
periodic table. ["Shell Model of Nucleus". HyperPhysics. Department of
Physics and Astronomy, Georgia State University.
Retrieved 2007-01-22.] [Emsley, John (2001). Nature's Building Blocks
((Hardcover, First Edition) ed.). Oxford University Press. pp. (pages
143,144,458). ISBN 0198503407.]
"We search for the island of stability because, like Mount Everest, it
is there. But, as with Everest, there is profound emotion, too,
infusing the scientific search to test a hypothesis. The quest for the
magic island shows us that science is far from being coldness and
calculation, as many people imagine, but is shot through with passion,
longing and romance. -- Oliver Sacks ["Greetings From the Island of
Stability", Opinion in the New York Times, February 8, 2004]
(2) Untriseptium, a hypothetical chemical element which has not been
observed to occur naturally, nor has it yet been synthesised. Due to
drip instabilities, it is not known if this element is physically
possible. Its atomic number is 137 and symbol is Uts. Calculations
have shown that 364Uts would be the most stable isotope. Unofficially
called Feynmanium because Richard Feynman noted that a simplistic
(Bohr model) interpretation of the relativistic Dirac equation runs
into problems with electron orbitals at Z > 1/α = 137, (the 1s
electrons would have to move faster than the speed of light)
suggesting that neutral atoms cannot exist beyond element 137, and
that a periodic table of elements based on electron orbitals therefore
breaks down at this point. However, a more rigorous analysis
calculates the limit to be Z ≈ 173. Alternatively, such ultra-heavy
atoms have negative energy ground states. Alternatively, there is
spontaneous production of electron-positron pairs between the nucleus
and innermost electron shell.
On Thu, Sep 3, 2009 at 6:51 AM, Chris Starling<chaosorder4 at gmail.com> wrote:
> Perhaps if the lengths of half-lives on a logarithmic scale cluster near a
> high node (stableish) and near a low node (unstableish), leaving a sea of
> non-used range, then the cutoff line could be placed tentatively and
> hopefully in the middle of that sea.
> On Wed, Sep 2, 2009 at 11:18 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>> I would be very happy to have sequences like these in the OEIS, if
>> only they were well-defined and not arbitrary. Stable at "the normal
>> room temperature conditions" is ill-defined; half-life over 10^20
>> years is arbitrary.
>> Perhaps isotopes by stability, except that that's not defined on the
>> lower end unless/until all (or all but one) of 'stable' isotopes are
>> found to have finite half-lives.
>> Charles Greathouse
>> Case Western Reserve University
>> On Wed, Sep 2, 2009 at 8:24 PM, <franktaw at netscape.net> wrote:
>> > See http://en.wikipedia.org/wiki/Bismuth-209. Bismuth 209 was long
>> > thought to be stable, but actually has a half-life of 1.9e19 years. It
>> > is likely that other isotopes will be found to be slightly unstable;
>> > perhaps all are (proton decay is still a theoretical concept).
>> > Frankly, I think this whole area ought to be left out of the OEIS; but
>> > as long as A007656 is present, I suppose there's no reason to exclude
>> > it.
>> > Franklin T. Adams-Watters
>> > -----Original Message-----
>> > From: David Wilson <davidwwilson at comcast.net>
>> > a(43) = 0 as well.
>> > I think "stable" once meant "will never spontaneously decay." The
>> > poster boy
>> > for stability was the proton.
>> > Wikipedia states that protons are now thought to have minimum half-life
>> > of
>> > 10^36 years, yet are still called stable.
>> > I don't find a defined half-life cutoff point where unstable becomes
>> > stable,
>> > maybe it's a matter of application.
>> > ----- Original Message -----
>> > From: "Antti Karttunen" <antti.karttunen at gmail.com>
>> >> Here is an idea for atomic elements related sequence that should
>> >> be reasonably well defined:
>> >> a(n) = The number of stable isotopes the element number n has.
>> >> If the information in Wikipedia is correct, the sequence should start
>> > as:
>> >> 2,2,2,1,2,2,2,3,1,3,...
>> >> Note that both a(83) ( http://en.wikipedia.org/wiki/Bismuth )
>> >> and a(92) ( http://en.wikipedia.org/wiki/Uranium ) should be 0.
>> >> (Or is it? Okay, we can speculate about the eventual decaying of
>> > protons,
>> >> but... Also, I mean stable at "the normal room temperature
>> > conditions",
>> >> not
>> >> inside
>> >> a particle accelerator.)
>> >> Cheers,
>> >> Antti.
>> > _______________________________________________
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