[seqfan] Re: Another chemistry related sequence?
franktaw at netscape.net
franktaw at netscape.net
Thu Sep 3 22:22:40 CEST 2009
Instead of "at least the half-life of U-238", how about "at least the
age of the universe"? That's about as unarbitrary as you can get in
this context.
Current estimates put the age of the universe at about 13 billion
years. From the list below, this leaves Thorium 232 (14.05 billion
years) as the only isotope in question by this criterion.
I think it is nearly certain that any new instabilities we find will be
at least on the order of trillions of years, and any new isotopes we
find will have half-lives at most on the order of seconds.
(Conceivably a little more in the "island of stability", but surely
well short of billions of years. Simple argument: if it had a
half-life that long, we would have found it.)
Franklin T. Adams-Watters
-----Original Message-----
From: Antti Karttunen <antti.karttunen at gmail.com>
On Thu, Sep 3, 2009 at 4:44 PM, <seqfan-request at list.seqfan.eu> wrote:
>Date: Wed, 2 Sep 2009 23:18:10 -0400
>From: Charles Greathouse <charles.greathouse at case.edu>
>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.
...
Yes, my proposed half-life limit, "at least the half-life of U-238"
is _arbitrary_, but its arbitrarity is not in anyway related to
our human culture (e.g. some {number of our fingers}^k amount of earth
years, etc.),
but to the half-life of the heaviest isotope of the heaviest
naturally occurring (not just in trace amounts like Pu-244, here as
elsewhere
in our galaxy?) element.
E.g., if we sent this sequence to some other star system, "they"
would almost certainly get what it is all about.
(As a(92)=1, and after that, all the rest are zeros.)
>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.
I guess including all the possible isotopes (also unstable)
would open another can of worms, as I surmise not all the most unstable
isotopes have not been found yet.
(E.g. http://en.wikipedia.org/wiki/Isotopes_of_boron tells that Boron-16
has half-life less than 190 picoseconds. What other isotopes with
extremely
short half-lives there could be, and thus very hard to detect?)
And as somebody in this thread commented, including just isotopes which
we
currently
know to be stable, leaves the possibility that later some of them are
found
to having extremely
long half-lives.
So, only one caveat which remains, that not all the stable and
"semi-stable"
isotopes of all elements have not been found yet? How plausible is that?
From the data in
http://www.nndc.bnl.gov/amdc/nubase/nubtab03.asc
(See page http://www.nndc.bnl.gov/amdc/web/nubase_en.html )
I count
karttu at andorinha:~/Matikka_papereita$ fgrep " stbl " nubtab03.asc | wc
-l
257 (isotopes marked as fully stable)
Then eight isotopes >= Half-life of Uranium-238:
karttu at andorinha:~/Matikka_papereita$ fgrep " Gy " nubtab03.asc
040 0190 40K -33535.20 0.19 1.251 Gy
0.011 4- 02 IS=0.0117 1;B-=89.28 13;B+=10.72 13
087 0370 87Rb -84597.795 0.012 49.23 Gy
0.22 3/2- 02 82Mi14t IS=27.83 2;B-=100
138 0570 138La -86525 4 102 Gy
1 5+ 03 IS=0.090 1;B+=65.6 5;B-=34.4 5
147 0620 147Sm -79272.1 2.4 106.0 Gy
1.1 7/2- 92 70Gu14t IS=14.99 18;A=100
176 0710 176Lu -53387.4 2.2 38.5 Gy
0.7 7- 98 03Gr02t IS=2.59 2;B-=100
187 0750 187Re -41215.7 1.4 41.2 Gy
0.2 5/2+ 91 01Ga01t IS=62.60 2;B-=100;A<0.0001
190 0780 190Pt -37323 6 650 Gy
30 0+ 03 IS=0.014 1;A=100;2B+ ?
232 0900 232Th 35448.3 2.0 14.05 Gy
0.06 0+ 91 95Bo18d IS=100.;A=100;SF=11e-10
3;24Ne+26Ne<2.78e-10;2B- ?
238 0920 238U 47308.9 1.9 4.468 Gy
0.003 0+ 02 91Tu02d IS=99.2745 106;A=100;SF=5.45e-5
7;2B-=2.2e-10 7
3 isotopes in Tera-years (10^12 yr range):
karttu at andorinha:~/Matikka_papereita$ fgrep " Ty " nubtab03.asc
115 0490 115In -89537 4 441 Ty
25 9/2+ 99 IS=95.71 5;B-=100
123 0520 123Te -89171.9 1.5 >600
Ty 1/2+ 94 96Al30t IS=0.89 3;EC=100
152 0640 152Gd -74714.2 2.5 108 Ty
8 0+ 97 IS=0.20 1;A=100;2B+ ?
6 isotopes in Peta-years (10^15 yr) range:
karttu at andorinha:~/Matikka_papereita$ fgrep " Py " nubtab03.asc
050 0230 50V -49221.6 1.0 150 Py
40 6+ 95 IS=0.250 4;B+=83 11;B-=17 11
113 0480 113Cd -89049.3 2.7 7.7 Py
0.3 1/2+ 98 IS=12.22 12;B-=100
144 0600 144Nd -83753.2 2.3 2.29 Py
0.16 0+ 01 IS=23.8 3;A=100
148 0620 148Sm -79342.2 2.4 7 Py
3 0+ 00 IS=11.24 10;A=100
174 0720 174Hf -55846.6 2.8 2.0 Py
0.4 0+ 99 IS=0.16 1;A=100;2B+ ?
186 0760 186Os -42999.5 1.4 2.0 Py
1.1 0+ 03 IS=1.59 3;A=100
8 isotopes in Exa-years (10^18 years) range:
karttu at andorinha:~/Matikka_papereita$ fgrep " Ey " nubtab03.asc
048 0200 48Ca -44214 4 53 Ey
17 0+ 95 00Br63t IS=0.187 21;2B-=?;B- ?
082 0340 82Se -77594.0 2.0 97 Ey
5 0+ 03 99Pi08t IS=8.73 22;2B-=100
096 0400 96Zr -85442.8 2.8 24 Ey
6 0+ 98 99Ar25t IS=2.80 9;2B-=100
100 0420 100Mo -86184 6 8.5 Ey
0.5 0+ 97 97Al02t IS=9.63 23;2B-=100
116 0480 116Cd -88719 3 30 Ey
4 0+ 01 03Da09t IS=7.49 18;2B-=100
130 0520 130Te -87351.4 1.9 790 Ey
100 0+ 01 96Ta04td IS=34.08 62;2B-=100
150 0600 150Nd -73690 3 6.7 Ey
0.7 0+ 96 97De40td IS=5.6 2;2B-=100
209 0830 209Bi -18258.5 1.4 19 Ey
2 9/2- 91 03De11td IS=100.;A=100
One isotope in Zetta-years (10^21 yr) range:
karttu at andorinha:~/Matikka_papereita$ fgrep " Zy " nubtab03.asc
076 0320 76Ge -73213.0 1.7 1.58 Zy
0.17 0+ 95 01Kl11t IS=7.61 38;2B-=100
And one isotope in Yotta-years (10^24 yr) range:
karttu at andorinha:~/Matikka_papereita$ fgrep " Yy " nubtab03.asc
128 0520 128Te -88992.1 1.7 2.2 Yy
0.3 0+ 01 96Ta04t IS=31.74 8;2B-=100
All in all, there are 27 known non-stable isotopes with half-lives >=
U-238:
karttu at andorinha:~/Matikka_papereita$ grep -c " [G|T|P|E|Z|Y]y "
nubtab03.asc
28
(K-40 = Potassium-40 has a half-life shorter than U-238).
Yours,
Antti Karttunen
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
> ----
>
> Message: 6
> Date: Thu, 3 Sep 2009 12:38:38 +0300
> From: Antti Karttunen <antti.karttunen at gmail.com>
> Subject: [seqfan] Another chemistry related sequence?
> To: seqfan at list.seqfan.eu
> Message-ID:
> <79be8a7d0909030238u11af94e1h2a95d021ab305a26 at mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
>
> On Thu, Sep 3, 2009 at 3:30 AM, <seqfan-request at list.seqfan.eu> wrote:
>
> >
> > Message: 10
> > Date: Wed, 02 Sep 2009 20:24:16 -0400
> > From: franktaw at netscape.net
> > Subject: [seqfan] Re: Another chemistry related sequence?
> > To: seqfan at list.seqfan.eu
> > Message-ID: <8CBFA44015A488B-4550-B63B at webmail-m012.sysops.aol.com>
> > Content-Type: text/plain; charset="us-ascii"; format=flowed
> >
> > 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.
> >
> >
>
> Hmm, it's getting complicated. Exactly defined sequences seem to mix
poorly
> with the real-life physics and chemistry. See also:
> http://en.wikipedia.org/wiki/Tellurium-128
> with the longest known half-life, 2.2?1024 years.
>
> So, instead, I propose an arbitrary cut-point:
> "Number of isotopes of the element with atomic number n, whose
half-life is
> >= half-life of Uranium-238"
> (i.e. 4.468x10^9 years). This age-limit is convenient also because
> it's an approximate age of the Earth and our Solar system.
> Then only problem would come if there were some isotope
> of another element than Uranium, with half-life so near to U-238
> that it would be beyond the reach of our measurements to determine
> whether it's shorter or longer than with U-238. But that is unlikely?
>
>
> Then, a(92)=1 and also a(83)=1.
>
> Question to Neil: Should I submit this sequence?
>
> Yours,
>
> Antti
>
>
>
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