{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation d'une décroissance radioactive\n", "\n", "(code sous licence creative commun CC BY-NC-SA BY Alexis Dendiével)\n" ] }, { "cell_type": "raw", "metadata": { "raw_mimetype": "text/restructuredtext" }, "source": [ ":download:`Télécharger le pdf <./exemple_2_decroissance_radioactive.pdf>`\n", "\n", ":download:`Télécharger le notebook <./exemple_2_decroissance_radioactive.ipynb>`\n", "\n", ":download:`Lancer le notebook sur binder (lent) `" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simulons une décroissance radioactive par un lancer de dès:\n", "\n", "- Un dé à 6 faces représente un atome radioactif. \n", "- Il se désintègre quand, lors d'un lancé, il indique 6.\n", "\n", "Sur un échantillon de plusieurs dés, la simulation consiste à retirer à chaque lancé les dés ayant indiqué 6. \n", "Nous traçons ensuite la courbe donnant le nombre d'atomes radioactifs en fonction du numéro de lancé.\n", "\n", "Ici encore, vous êtes juste invités à excécuter le programme." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# programme de simulation de décroissance radioactive\n", "# par le jet de dés\n", "\n", "# importations de fonctions utiles\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "from random import randint\n", "\n", "# fonction permettant de lancer la simulation pour un\n", "# nombre n d'atomes\n", "def simulation(n):\n", " # initialisation des données\n", " nombrelance = 0\n", " temps = [0]\n", " radioactifs = [n]\n", "\n", " # coeur du programme\n", " while n > 0:\n", " desintegration = 0\n", " for i in range(n):\n", " tirage = randint(1,6)\n", " if tirage == 6:\n", " desintegration = desintegration + 1\n", " n = n - desintegration\n", " nombrelance = nombrelance + 1\n", " temps.append(nombrelance)\n", " radioactifs.append(n)\n", "\n", " # affichage\n", " plt.figure()\n", " plt.plot(temps, radioactifs)\n", " plt.grid()\n", " plt.xlabel(\"temps\")\n", " plt.ylabel(\"nombre d'atomes radioactifs\")\n", " plt.show()\n", " plt.close()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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