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    {
      "cell_type": "code",
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      "source": [
        "# You need to import the following modules\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wYmlWQi9fAAm"
      },
      "source": [
        "# **Test 02**\n",
        "\n",
        "## In this test, you are asked to write some scripts which will help you to solve problem related to the Bethe-Bloch formula, giving the stopping power of radiation in a given medium, or also known as \"Linear Energy Transfer\" (LET):\n",
        "\n",
        "## $-\\frac{dE}{dx}=\\frac{4\\pi}{m_{e}.c^{2}}.\\frac{n.z^{2}}{\\beta^{2}}.(\\frac{e^{2}}{4\\pi\\epsilon_{0}})^{2}.[ln(\\frac{2m_{e}c^{2}\\beta^{2}}{I.(1-\\beta^{2})})-\\beta^{2}]$\n",
        "\n",
        "Where could define each parameters:\n",
        "\n",
        "$𝒆$: electron charge, \n",
        "\n",
        "$m_{e}$: rest electron mass,\n",
        "\n",
        "$z$: atomic number of incident particle (for $e$ : $z=1$),\n",
        "\n",
        "$\\beta=\\frac{v}{c}$: relative speed of incident particle,\n",
        "\n",
        "$I$: mean excitation energy of the target medium,\n",
        "\n",
        "$n=\\frac{N_{A}.Z.\\rho}{M}$: electronic density of the target medium"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Task 1\n",
        "You need to define for a given kinetic energy of incident particle, the relative speed $\\beta=\\frac{v}{c}$ as a function of rest energy and kinetic energy.\n",
        "\n",
        "To do this, you need to use the relativistic general relationship: $E=T+m_{0}c^{2}=\\gamma.m_{0}c^{2}$\n",
        "Where : $\\gamma = \\sqrt{1-\\beta^{2}}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Write here your script with python giving the value of Beta\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Task 2\n",
        "Let's consider now the water as target medium. Knowing that under normal conditions of pressure and temperature, water density is $\\rho_{wtr}=1.0[\\frac{g}{cm^{3}}]$, and its molar mass is $M_{wtr}=18[\\frac{g}{mol}]$. \n",
        "\n",
        "Find the electronic density of the water $n$ as defined above in the Bethe-Bloch formula section.\n",
        "\n",
        "$N_{A}=6.022 \\times 10^{23}[\\frac{atom}{mol}]$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Write here your script with python giving the value of electronic density of water\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Task 3\n",
        "We know that the mean excitation energy of water is given by $I=75[eV]$.\n",
        "Find the LET of a $\\beta^{-}$ particle with a kinetic energy $T_{\\beta}=1.0[MeV]$, by using the relativistic Bethe-Bloch formula given above."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": [
        "# Write here your script with python giving the value of the LET of 1MeV Beta- particle\n",
        "\n",
        "\n"
      ]
    }
  ],
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