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désintégration audioactive.md
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@@ -313,14 +313,116 @@ header-auto-numbering:
Avant de continuer, il est nécessaire de poser une liste particulières de 92 atomes.
On a défini plus tôt ce qu'était un [[désintégration audioactive#^def-atome|atome]].
On peut alors décrire 92 atomes. Il est trivial de montrer que chacune de ces 92 chaînes est bien un atome (à l'aide du [[désintégration audioactive#^theoreme-de-decoupage|théorème de découpage]]).
Par analogie avec le tableau périodique des éléments
Conway leur donne des noms d'éléments (de l'hydrogène à l'uranium, ce qui fait bien 92 éléments).
> [!info]- Liste des éléments
> | élément | nom | dérivée | chaîne | dérivée |
> | ------- | --- | ---------------- | ------------------------------------------ | ---------------------------------------------------- |
> | 1 | H | H (stable) | 22 | 22 |
> | 2 | He | Hf Pa H Ca Li | 13112221133211322112211213322112 | 11132132212312211322212221121123222112 |
> | 3 | Li | He | 312211322212221121123222112 | 13112221133211322112211213322112 |
> | 4 | Be | Ge Ca Li | 111312211312113221133211322112211213322112 | 3113112221131112211322212312211322212221121123222112 |
> | 5 | B | Be | 1321132122211322212221121123222112 | 111312211312113221133211322112211213322112 |
> | 6 | C | B | 3113112211322112211213322112 | 1321132122211322212221121123222112 |
> | 7 | N | C | 111312212221121123222112 | 3113112211322112211213322112 |
> | 8 | O | N | 132112211213322112 | 111312212221121123222112 |
> | 9 | F | O | 31121123222112 | 132112211213322112 |
> | 10 | Ne | F | 111213322112 | 31121123222112 |
> | 11 | Na | Ne | 123222112 | 111213322112 |
> | 12 | Mg | Pm Na | 3113322112 | 132123222112 |
> | 13 | Al | Mg | 1113222112 | 3113322112 |
> | 14 | Si | Al | 1322112 | 1113222112 |
> | 15 | P | Ho Si | 311311222112 | 13211321322112 |
> | 16 | S | P | 1113122112 | 311311222112 |
> | 17 | Cl | S | 132112 | 1113122112 |
> | 18 | Ar | Cl | 3112 | 132112 |
> | 19 | K | Ar | 1112 | 3112 |
> | 20 | Ca | K | 12 | 1112 |
> | 21 | Sc | Ho Pa H Ca Co | 3113112221133112 | 132113213221232112 |
> | 22 | Ti | Sc | 11131221131112 | 3113112221133112 |
> | 23 | V | Ti | 13211312 | 11131221131112 |
> | 24 | Cr | V | 31132 | 13211312 |
> | 25 | Mn | Cr Si | 111311222112 | 311321322112 |
> | 26 | Fe | Mn | 13122112 | 111311222112 |
> | 27 | Co | Fe | 32112 | 13122112 |
> | 28 | Ni | Zn Co | 11133112 | 31232112 |
> | 29 | Cu | Ni | 131112 | 11133112 |
> | 30 | Zn | Cu | 312 | 131112 |
> | 31 | Ga | Eu Ca Ac H Ca Zn | 13221133122211332 | 11132221231132212312 |
> | 32 | Ge | Ho Ga | 31131122211311122113222 | 132113213221133122211332 |
> | 33 | As | Ge Na | 11131221131211322113322112 | 31131122211311122113222123222112 |
> | 34 | Se | As | 13211321222113222112 | 11131221131211322113322112 |
> | 35 | Br | Se | 3113112211322112 | 13211321222113222112 |
> | 36 | Kr | Br | 11131221222112 | 3113112211322112 |
> | 37 | Rb | Kr | 1321122112 | 11131221222112 |
> | 38 | Sr | Rb | 3112112 | 1321122112 |
> | 39 | Y | Sr U | 1112133 | 31121123 |
> | 40 | Zr | Y H Ca Tc | 12322211331222113112211 | 11121332212311322113212221 |
> | 41 | Nb | Er Zr | 1113122113322113111221131221 | 31131122212322211331222113112211 |
> | 42 | Mo | Nb | 13211322211312113211 | 1113122113322113111221131221 |
> | 43 | Tc | Mo | 311322113212221 | 13211322211312113211 |
> | 44 | Ru | Eu Ca Tc | 132211331222113112211 | 111322212311322113212221 |
> | 45 | Rh | Ho Ru | 311311222113111221131221 | 1321132132211331222113112211 |
> | 46 | Pd | Rh | 111312211312113211 | 311311222113111221131221 |
> | 47 | Ag | Pd | 132113212221 | 111312211312113211 |
> | 48 | Cd | Ag | 3113112211 | 132113212221 |
> | 49 | In | Cd | 11131221 | 3113112211 |
> | 50 | Sn | In | 13211 | 11131221 |
> | 51 | Sb | Pm Sn | 3112221 | 13213211 |
> | 52 | Te | Eu Ca Sb | 1322113312211 | 1113222123112221 |
> | 53 | I | Ho Te | 311311222113111221 | 13211321322113312211 |
> | 54 | Xe | I | 11131221131211 | 311311222113111221 |
> | 55 | Cs | Xe | 13211321 | 11131221131211 |
> | 56 | Ba | Cs | 311311 | 13211321 |
> | 57 | La | Ba | 11131 | 311311 |
> | 58 | Ce | La H Ca Co | 1321133112 | 11131221232112 |
> | 59 | Pr | Ce | 31131112 | 1321133112 |
> | 60 | Nd | Pr | 111312 | 31131112 |
> | 61 | Pm | Nd | 132 | 111312 |
> | 62 | Sm | Pm Ca Zn | 311332 | 13212312 |
> | 63 | Eu | Sm | 1113222 | 311332 |
> | 64 | Gd | Eu Ca Co | 13221133112 | 11132221232112 |
> | 65 | Tb | Ho Gd | 3113112221131112 | 132113213221133112 |
> | 66 | Dy | Tb | 111312211312 | 3113112221131112 |
> | 67 | Ho | Dy | 1321132 | 111312211312 |
> | 68 | Er | Ho Pm | 311311222 | 1321132132 |
> | 69 | Tm | Er Ca Co | 11131221133112 | 3113112221232112 |
> | 70 | Yb | Tm | 1321131112 | 11131221133112 |
> | 71 | Lu | Yb | 311312 | 1321131112 |
> | 72 | Hf | Lu | 11132 | 311312 |
> | 73 | Ta | Hf Pa H Ca W | 13112221133211322112211213322113 | 11132132212312211322212221121123222113 |
> | 74 | W | Ta | 312211322212221121123222113 | 13112221133211322112211213322113 |
> | 75 | Re | Ge Ca W | 111312211312113221133211322112211213322113 | 3113112221131112211322212312211322212221121123222113 |
> | 76 | Os | Re | 1321132122211322212221121123222113 | 111312211312113221133211322112211213322113 |
> | 77 | Ir | Os | 3113112211322112211213322113 | 1321132122211322212221121123222113 |
> | 78 | Pt | Ir | 111312212221121123222113 | 3113112211322112211213322113 |
> | 79 | Au | Pt | 132112211213322113 | 111312212221121123222113 |
> | 80 | Hg | Au | 31121123222113 | 132112211213322113 |
> | 81 | Tl | Hg | 111213322113 | 31121123222113 |
> | 82 | Pb | Tl | 123222113 | 111213322113 |
> | 83 | Bi | Pm Pb | 3113322113 | 132123222113 |
> | 84 | Po | Bi | 1113222113 | 3113322113 |
> | 85 | At | Po | 1322113 | 1113222113 |
> | 86 | Rn | Ho At | 311311222113 | 13211321322113 |
> | 87 | Fr | Rn | 1113122113 | 311311222113 |
> | 88 | Ra | Fr | 132113 | 1113122113 |
> | 89 | Ac | Ra | 3113 | 132113 |
> | 90 | Th | Ac | 1113 | 3113 |
> | 91 | Pa | Th | 13 | 1113 |
> | 92 | U | Pa | 3 | 13 |
## Théorèmes
> [!proposition]+ Théorème chimique
> 1. les descendents
> 1. les descendents de chacun des 92 éléments sont des composés de ces éléments
> Autrement dit : $\forall A \text{ élément},\quad A \longrightarrow X_1\cdot X_2\cdot \cdots \quad \text{ où }X_1,X_2,\dots \text{ sont des éléments}$
> 2. Tous les déscendants suffisament âgés de chacun des éléments (autres que l'Hydrogène $22$) contiennent simultanément les 92 éléments.
> Autrement dit : $\forall A \text{ élément},\quad \exists n\in \mathbb{N},\quad A \longrightarrow^{(n)} X \quad \text{où } X \text{ contient tous les 92 éléments}$
## Tableau des éléments