Radioactivite — Quiz — Decroissance Radioactive

{
  "quiz_title": "Decroissance Radioactive",
  "quiz_slug": "06_decroissance_radioactive_quiz",
  "quiz_description": "Quiz Edu509 : Decroissance Radioactive",
  "quiz_settings": {
    "time_limit": {
      "time_value": 0,
      "time_type": "minutes"
    },
    "hide_quiz_time_display": false,
    "attempts_allowed": 0,
    "passing_grade": 70,
    "max_questions_for_answer": 0,
    "questions_order": "rand",
    "hide_question_number_overview": false,
    "short_answer_characters_limit": 200
  },
  "questions": [
    {
      "question_order": 1,
      "question_title": "Quelle est la formule mathématique de la loi de décroissance radioactive ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La loi de décroissance radioactive s'écrit \\\\( N(t) = N_0 e^{-\\\\lambda t} \\\\), où \\\\( N_0 \\\\) est le nombre initial de noyaux et \\\\( \\\\lambda \\\\) la constante de décroissance.",
      "answers": [
        {
          "answer_title": "\\\\( N(t) = N_0 e^{-\\\\lambda t} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( N(t) = N_0 + \\\\lambda t \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( N(t) = N_0 - \\\\lambda t \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( N(t) = N_0 e^{\\\\lambda t} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 2,
      "question_title": "Un échantillon contient 2 000 noyaux d’un isotope dont la demi-vie est de 20 minutes. Combien de noyaux restent après 1 heure ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après 1 heure (3 demi-vies), il reste \\\\( 2 000 \\\\times (1/2)^3 = 250 \\\\) noyaux.",
      "answers": [
        {
          "answer_title": "250",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1 000",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "500",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "1 500",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 3,
      "question_title": "Quelle est la relation correcte entre la demi-vie \\\\( T_{1/2} \\\\) et la constante de décroissance \\\\( \\\\lambda \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La demi-vie est donnée par \\\\( T_{1/2} = \\\\frac{\\\\ln 2}{\\\\lambda} \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( T_{1/2} = \\\\frac{\\\\ln 2}{\\\\lambda} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( T_{1/2} = \\\\lambda \\\\ln 2 \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( T_{1/2} = \\\\frac{1}{\\\\lambda} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( T_{1/2} = \\\\lambda^2 \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 4,
      "question_title": "Si la constante de décroissance d’un isotope est \\\\( 0{,}005\\\\ \\\\mathrm{s}^{-1} \\\\), quelle est sa demi-vie en secondes ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La demi-vie est \\\\( T_{1/2} = \\\\frac{0{,}693}{0{,}005} = 138,6\\\\ \\\\mathrm{s} \\\\).",
      "answers": [
        {
          "answer_title": "138,6",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "0,1386",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "13,86",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "693",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 5,
      "question_title": "Après deux demi-vies, quelle fraction des noyaux initiaux reste-t-il ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après deux demi-vies, la fraction restante est \\\\( (1/2)^2 = 1/4 \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( \\\\frac{1}{4} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( \\\\frac{1}{2} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( \\\\frac{1}{8} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( \\\\frac{3}{4} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 6,
      "question_title": "Un échantillon contient 10 000 noyaux d’un isotope dont la demi-vie est de 15 minutes. Combien de noyaux restent après 45 minutes ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après 45 minutes (3 demi-vies), il reste \\\\( 10 000 \\\\times (1/2)^3 = 1 250 \\\\) noyaux.",
      "answers": [
        {
          "answer_title": "1 250",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "5 000",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "2 500",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "3 333",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 7,
      "question_title": "Quelle est l’unité de l’activité radioactive dans le Système International ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’activité radioactive s’exprime en becquerel (Bq) dans le Système International.",
      "answers": [
        {
          "answer_title": "Becquerel (Bq)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Gray (Gy)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Sievert (Sv)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Curie (Ci)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 8,
      "question_title": "Laquelle des affirmations suivantes est correcte concernant la décroissance radioactive ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La décroissance radioactive est aléatoire pour chaque noyau mais suit une loi statistique exponentielle sur un grand nombre de noyaux.",
      "answers": [
        {
          "answer_title": "Elle est un phénomène aléatoire pour chaque noyau, mais prévisible statistiquement sur un grand nombre de noyaux.",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Elle est parfaitement prévisible pour chaque noyau individuel.",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Elle suit une décroissance linéaire.",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Elle ne dépend pas du temps.",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 9,
      "question_title": "Si l’activité initiale d’un échantillon est de 8 Bq et la demi-vie de 10 minutes, quelle sera l’activité après 20 minutes ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après 2 demi-vies, l’activité est divisée par 4 : \\\\( 8/4 = 2 \\\\) Bq.",
      "answers": [
        {
          "answer_title": "2 Bq",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "4 Bq",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "1 Bq",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "8 Bq",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 10,
      "question_title": "Quelle(s) grandeur(s) diminue(nt) exponentiellement lors de la décroissance radioactive ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Le nombre de noyaux restants et l’activité diminuent exponentiellement, mais \\\\( \\\\lambda \\\\) et \\\\( T_{1/2} \\\\) sont constants.",
      "answers": [
        {
          "answer_title": "Nombre de noyaux restants \\\\( N(t) \\\\)",
          "is_correct": false,
          "answer_order": 1
        },
        {
          "answer_title": "Activité \\\\( A(t) \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Constante de décroissance \\\\( \\\\lambda \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Demi-vie \\\\( T_{1/2} \\\\)",
          "is_correct": true,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 11,
      "question_title": "Un échantillon a une activité de 0,5 Bq après 3 600 s. Si \\\\( \\\\lambda = 0{,}000385\\\\ \\\\mathrm{s}^{-1} \\\\), combien de noyaux restent à cet instant ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Le nombre de noyaux restants est \\\\( N = \\\\frac{A}{\\\\lambda} = \\\\frac{0,5}{0,000385} \\\\approx 1 298 \\\\).",
      "answers": [
        {
          "answer_title": "1 298",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1 250",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "1 000",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "2 000",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 12,
      "question_title": "Quelle est la probabilité qu’un noyau se désintègre pendant une durée très courte \\\\( \\\\Delta t \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La probabilité de désintégration pendant \\\\( \\\\Delta t \\\\) est \\\\( \\\\lambda \\\\Delta t \\\\) pour un intervalle très court.",
      "answers": [
        {
          "answer_title": "\\\\( \\\\lambda \\\\Delta t \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( \\\\lambda / \\\\Delta t \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( \\\\Delta t / \\\\lambda \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( \\\\lambda^2 \\\\Delta t \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 13,
      "question_title": "Si on commence avec 5 000 noyaux et qu’il en reste 1 250 après un certain temps, combien de demi-vies se sont écoulées ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après 2 demi-vies, il reste \\\\( 5 000 \\\\times (1/2)^2 = 1 250 \\\\) noyaux.",
      "answers": [
        {
          "answer_title": "2",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "1",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "4",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 14,
      "question_title": "Laquelle des propositions suivantes est une erreur courante en calculant la décroissance radioactive ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La formule \\\\( N(t) = N_0 - \\\\lambda t \\\\) est fausse, la décroissance est exponentielle, pas linéaire.",
      "answers": [
        {
          "answer_title": "Utiliser la formule \\\\( N(t) = N_0 - \\\\lambda t \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Utiliser la formule \\\\( N(t) = N_0 e^{-\\\\lambda t} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Vérifier les unités avant de calculer",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Utiliser \\\\( T_{1/2} = \\\\frac{\\\\ln 2}{\\\\lambda} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 15,
      "question_title": "Un isotope a une demi-vie de 30 minutes. Quelle fraction des noyaux initiaux reste-t-il après 1 h 30 min ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "1 h 30 min = 3 demi-vies, donc la fraction restante est \\\\( (1/2)^3 = 1/8 \\\\).",
      "answers": [
        {
          "answer_title": "\\\\( \\\\frac{1}{8} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "\\\\( \\\\frac{1}{2} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "\\\\( \\\\frac{1}{4} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "\\\\( \\\\frac{1}{16} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 16,
      "question_title": "Si la demi-vie d’un isotope est de 900 s, quelle est la valeur de \\\\( \\\\lambda \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La constante de décroissance est \\\\( \\\\lambda = \\\\frac{0,693}{900} = 0,00077\\\\ \\\\mathrm{s}^{-1} \\\\).",
      "answers": [
        {
          "answer_title": "0,00077 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "0,0077 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "0,000693 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "0,009 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 17,
      "question_title": "L’activité d’un échantillon est-elle proportionnelle au nombre de noyaux restants ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "L’activité est donnée par \\\\( A(t) = \\\\lambda N(t) \\\\), donc elle est proportionnelle au nombre de noyaux restants.",
      "answers": [
        {
          "answer_title": "Oui",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Non",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "Seulement au début",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Seulement à la fin",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 18,
      "question_title": "Après combien de demi-vies reste-t-il moins de 10 % des noyaux initiaux ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "Après 4 demi-vies, il reste \\\\( (1/2)^4 = 1/16 \\\\approx 6,25\\\\% \\\\), donc moins de 10\\\\%.",
      "answers": [
        {
          "answer_title": "4",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "2",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "3",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "5",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 19,
      "question_title": "Quelle(s) grandeur(s) reste(nt) constante(s) lors de la décroissance radioactive ?",
      "question_type": "multiple_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "La constante de décroissance et la demi-vie restent constantes, tandis que \\\\( N(t) \\\\) et \\\\( A(t) \\\\) diminuent.",
      "answers": [
        {
          "answer_title": "Constante de décroissance \\\\( \\\\lambda \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "Demi-vie \\\\( T_{1/2} \\\\)",
          "is_correct": true,
          "answer_order": 2
        },
        {
          "answer_title": "Nombre de noyaux restants \\\\( N(t) \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "Activité \\\\( A(t) \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    },
    {
      "question_order": 20,
      "question_title": "Un échantillon a une activité initiale de 7,7 Bq et contient 10 000 noyaux. Quelle est la valeur de \\\\( \\\\lambda \\\\) ?",
      "question_type": "single_choice",
      "question_mark": 1,
      "answer_required": true,
      "randomize_question": false,
      "show_question_mark": true,
      "question_description": "",
      "question_explanation": "On a \\\\( \\\\lambda = \\\\frac{A_0}{N_0} = \\\\frac{7,7}{10 000} = 0,00077\\\\ \\\\mathrm{s}^{-1} \\\\).",
      "answers": [
        {
          "answer_title": "0,00077 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": true,
          "answer_order": 1
        },
        {
          "answer_title": "0,0077 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 2
        },
        {
          "answer_title": "0,000693 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 3
        },
        {
          "answer_title": "0,007 \\\\( \\\\mathrm{s}^{-1} \\\\)",
          "is_correct": false,
          "answer_order": 4
        }
      ]
    }
  ]
}