5.5.1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide_input": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import math\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit(x,y):\n",
    "    A = np.vstack([x, np.ones(len(x))]).T\n",
    "    a,b = np.linalg.lstsq(A, y, rcond=None)[0]\n",
    "    return a,b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hide_input": false
   },
   "source": [
    "# Работа 5.1\n",
    "# Измерение коэффциента ослабления потока $\\gamma$-лучей в веществе и определение их энергии\n",
    "\n",
    "С помощью сцинтилляционного счетчика измеряются линейные коэффициенты ослабления потока $\\gamma$-лучей в свинце, железе и алюминии; по их величине определяется энергия $\\gamma$-квантов.\n",
    "Гамма-лучи возникают при переходе возбужденных ядер из одного\n",
    "энергетического состояния в другое, более низкое. Энергия $\\gamma$-квантов обычно заключена между несколькими десятками килоэлектронвольт и несколькими миллионами электрон-вольт. Гамма-кванты не несут электрического заряда, их масса равна нулю. Проходя через вещество, пучок $\\gamma$-квантов постепенно ослабляется. Ослабление происходит по экспоненциальному закону, который может быть записан в\n",
    "двух эквивалентных формах:\n",
    "\n",
    "\\begin{equation}\n",
    "I = I_0e^{\\mu l}\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "I = I_0e^{\\mu' m_1}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$I,I_0$ - интенсивности прошедшего и падающего излучений\n",
    "$l$ - длина пути, пройденного $\\gamma$ - лучей, $\\mu, \\mu'$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Тогда $\\mu$ определяется:\n",
    "$$\n",
    "\\mu = \\frac{1}{l}ln\\frac{N_0}{N}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задание\n",
    "1. Включите пересчетный прибор и высоковольтный выпрямитель. Дайте им прогреться в течение 5-10 минут\n",
    "2. Убедитесь в том, что установка чувствует $\\gamma$-лучи. Для этого подайте на ФЭУ напряжение, указанное на установке. Измерьте скорость счета при полностью открытом коллиматоре, а затем при коллиматоре, закрытом свинцовой пробкой. Скорость счета должна резко уменьшиться. Чтобы убедиться в работоспособности установки, повторите эту процедуру 23 раза."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. При вычислении $N_0$ и $N$ из показаний прибора необходимо вычитать он, который обусловлен шумом ФЭУ и посторонними частицами: космическим излучением, $\\gamma$-квантами от соседних источников, квантами, рассеянными на стенах комнаты и в стенках прибора и т.д."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$N_0 $ без преграды</th>\n",
       "      <th>шум</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>95429.00</td>\n",
       "      <td>210.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>94740.00</td>\n",
       "      <td>229.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>95331.00</td>\n",
       "      <td>189.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>95167.00</td>\n",
       "      <td>209.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Средняя</th>\n",
       "      <td>95166.75</td>\n",
       "      <td>209.25</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         $N_0 $ без преграды     шум\n",
       "0                   95429.00  210.00\n",
       "1                   94740.00  229.00\n",
       "2                   95331.00  189.00\n",
       "3                   95167.00  209.00\n",
       "Средняя             95166.75  209.25"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_0 = np.array([[95429,210],\n",
    "[94740,229],\n",
    "[95331,189],\n",
    "[95167,209]])\n",
    "data = pd.DataFrame(data_0, \n",
    "                    index = np.arange(1,len(data_0)+1,1),\n",
    "                    columns = ['$N_0 $ без преграды','шум'])\n",
    "\n",
    "data = data.append({'$N_0 $ без преграды':np.mean(data_0[:,0]),'шум':np.mean(data_0[:,1])}, ignore_index=True)\n",
    "data = data.rename(index = {len(data)-1:'Средняя'})\n",
    "N0 = data.iloc[4,0]-data.iloc[4,1]\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N_0 без шума = 94957.5\n"
     ]
    }
   ],
   "source": [
    "print('N_0 без шума','=',N0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "def create_table (data,lenth_of_material,average_value_without_noize):\n",
    "    table = pd.DataFrame({'data_0':data,'lenth':np.arange(lenth_of_material,(len(data)+1)*lenth_of_material,lenth_of_material),\n",
    "                         },\n",
    "                         index = np.arange(1,len(data)+1,1))\n",
    "    \n",
    "    table = table.assign(data_1 = lambda x: x.data_0 - 209)\n",
    "    data_2 = pd.Series(index = np.arange(1,len(data)+1,1))\n",
    "    \n",
    "    for i in range(len(data)):\n",
    "        data_2[i+1] = math.log(average_value_without_noize/table['data_1'][i+1])\n",
    "\n",
    "    table['ln(N)'] = data_2\n",
    "    \n",
    "    mu = pd.Series(index = np.arange(1,len(data)+1,1))\n",
    "    for i in range(len(data)):\n",
    "        mu[i+1] = 1/table['lenth'][i+1]*math.log(average_value_without_noize/table['data_1'][i+1])\n",
    "    table['$\\mu$'] = mu\n",
    "    table = table.rename(columns = {'lenth':'Длина(cm)','data_0':'N с шумом','data_1':'N без шума'})\n",
    "    return table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
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   "outputs": [
    {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>Материал</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.00</td>\n",
       "      <td>Алюминий</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.45</td>\n",
       "      <td>Свинец</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.00</td>\n",
       "      <td>Железо</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.00</td>\n",
       "      <td>Дерево</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Длина(cm)  Материал\n",
       "1       2.00  Алюминий\n",
       "2       0.45    Свинец\n",
       "3       1.00    Железо\n",
       "4       2.00    Дерево"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lenth = pd.DataFrame ({'Материал':['Алюминий','Свинец','Железо','Дерево'],\n",
    "                       'Длина(cm)':[2,0.45,1,2]},\n",
    "                     index = np.arange(1,5,1))\n",
    "lenth"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "source": [
    "### Данные"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Аллюминий"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>61200</td>\n",
       "      <td>2</td>\n",
       "      <td>60991</td>\n",
       "      <td>0.442703</td>\n",
       "      <td>0.221352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>41053</td>\n",
       "      <td>4</td>\n",
       "      <td>40844</td>\n",
       "      <td>0.843669</td>\n",
       "      <td>0.210917</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>27267</td>\n",
       "      <td>6</td>\n",
       "      <td>27058</td>\n",
       "      <td>1.255447</td>\n",
       "      <td>0.209241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18350</td>\n",
       "      <td>8</td>\n",
       "      <td>18141</td>\n",
       "      <td>1.655255</td>\n",
       "      <td>0.206907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12489</td>\n",
       "      <td>10</td>\n",
       "      <td>12280</td>\n",
       "      <td>2.045458</td>\n",
       "      <td>0.204546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8583</td>\n",
       "      <td>12</td>\n",
       "      <td>8374</td>\n",
       "      <td>2.428298</td>\n",
       "      <td>0.202358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5764</td>\n",
       "      <td>14</td>\n",
       "      <td>5555</td>\n",
       "      <td>2.838731</td>\n",
       "      <td>0.202766</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$\n",
       "1      61200          2       60991  0.442703  0.221352\n",
       "2      41053          4       40844  0.843669  0.210917\n",
       "3      27267          6       27058  1.255447  0.209241\n",
       "4      18350          8       18141  1.655255  0.206907\n",
       "5      12489         10       12280  2.045458  0.204546\n",
       "6       8583         12        8374  2.428298  0.202358\n",
       "7       5764         14        5555  2.838731  0.202766"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all = create_table([\n",
    "    61200,\n",
    "    41053,\n",
    "    27267,\n",
    "    18350,\n",
    "    12489,\n",
    "    8583,\n",
    "    5764],2,N0)\n",
    "all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu_all_aver = 0.2082981857167199\n",
      "Cреднеквадратичное отклонение = 0.0065833110872393075\n"
     ]
    }
   ],
   "source": [
    "mu_all_aver = np.mean(all.iloc[:,4])\n",
    "mu_all_delta = all.iloc[:,4] - mu_all_aver\n",
    "all['$\\delta \\mu$'] = mu_all_delta\n",
    "print('mu_all_aver =',mu_all_aver)\n",
    "print('Cреднеквадратичное отклонение =',np.std(all.iloc[:,4], ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\delta \\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>61200</td>\n",
       "      <td>2</td>\n",
       "      <td>60991</td>\n",
       "      <td>0.442703</td>\n",
       "      <td>0.221352</td>\n",
       "      <td>0.013053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>41053</td>\n",
       "      <td>4</td>\n",
       "      <td>40844</td>\n",
       "      <td>0.843669</td>\n",
       "      <td>0.210917</td>\n",
       "      <td>0.002619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>27267</td>\n",
       "      <td>6</td>\n",
       "      <td>27058</td>\n",
       "      <td>1.255447</td>\n",
       "      <td>0.209241</td>\n",
       "      <td>0.000943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18350</td>\n",
       "      <td>8</td>\n",
       "      <td>18141</td>\n",
       "      <td>1.655255</td>\n",
       "      <td>0.206907</td>\n",
       "      <td>-0.001391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12489</td>\n",
       "      <td>10</td>\n",
       "      <td>12280</td>\n",
       "      <td>2.045458</td>\n",
       "      <td>0.204546</td>\n",
       "      <td>-0.003752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8583</td>\n",
       "      <td>12</td>\n",
       "      <td>8374</td>\n",
       "      <td>2.428298</td>\n",
       "      <td>0.202358</td>\n",
       "      <td>-0.005940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5764</td>\n",
       "      <td>14</td>\n",
       "      <td>5555</td>\n",
       "      <td>2.838731</td>\n",
       "      <td>0.202766</td>\n",
       "      <td>-0.005532</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$  $\\delta \\mu$\n",
       "1      61200          2       60991  0.442703  0.221352      0.013053\n",
       "2      41053          4       40844  0.843669  0.210917      0.002619\n",
       "3      27267          6       27058  1.255447  0.209241      0.000943\n",
       "4      18350          8       18141  1.655255  0.206907     -0.001391\n",
       "5      12489         10       12280  2.045458  0.204546     -0.003752\n",
       "6       8583         12        8374  2.428298  0.202358     -0.005940\n",
       "7       5764         14        5555  2.838731  0.202766     -0.005532"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Свинец"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>54145</td>\n",
       "      <td>0.45</td>\n",
       "      <td>53936</td>\n",
       "      <td>0.565631</td>\n",
       "      <td>1.256958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>32575</td>\n",
       "      <td>0.90</td>\n",
       "      <td>32366</td>\n",
       "      <td>1.076321</td>\n",
       "      <td>1.195912</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18100</td>\n",
       "      <td>1.35</td>\n",
       "      <td>17891</td>\n",
       "      <td>1.669132</td>\n",
       "      <td>1.236394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10354</td>\n",
       "      <td>1.80</td>\n",
       "      <td>10145</td>\n",
       "      <td>2.236448</td>\n",
       "      <td>1.242471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6213</td>\n",
       "      <td>2.25</td>\n",
       "      <td>6004</td>\n",
       "      <td>2.761004</td>\n",
       "      <td>1.227113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4185</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3976</td>\n",
       "      <td>3.173153</td>\n",
       "      <td>1.175242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2504</td>\n",
       "      <td>3.15</td>\n",
       "      <td>2295</td>\n",
       "      <td>3.722697</td>\n",
       "      <td>1.181808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1666</td>\n",
       "      <td>3.60</td>\n",
       "      <td>1457</td>\n",
       "      <td>4.177050</td>\n",
       "      <td>1.160292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1152</td>\n",
       "      <td>4.05</td>\n",
       "      <td>943</td>\n",
       "      <td>4.612118</td>\n",
       "      <td>1.138795</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$\n",
       "1      54145       0.45       53936  0.565631  1.256958\n",
       "2      32575       0.90       32366  1.076321  1.195912\n",
       "3      18100       1.35       17891  1.669132  1.236394\n",
       "4      10354       1.80       10145  2.236448  1.242471\n",
       "5       6213       2.25        6004  2.761004  1.227113\n",
       "6       4185       2.70        3976  3.173153  1.175242\n",
       "7       2504       3.15        2295  3.722697  1.181808\n",
       "8       1666       3.60        1457  4.177050  1.160292\n",
       "9       1152       4.05         943  4.612118  1.138795"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pb =  create_table([\n",
    "    54145,\n",
    "    32575,\n",
    "    18100,\n",
    "    10354,\n",
    "    6213,\n",
    "    4185,\n",
    "    2504,\n",
    "    1666,\n",
    "    1152],0.45,N0)\n",
    "pb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu_pb_aver = 1.2016649994623623\n",
      "Cреднеквадратичное отклонение = 0.040875085150684935\n"
     ]
    }
   ],
   "source": [
    "mu_pb_aver = np.mean(pb.iloc[:,4])\n",
    "mu_pb_delta = pb.iloc[:,4] - mu_pb_aver\n",
    "pb['$\\delta \\mu$'] = mu_pb_delta\n",
    "print('mu_pb_aver =',mu_pb_aver)\n",
    "print('Cреднеквадратичное отклонение =',np.std(pb.iloc[:,4], ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\delta \\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>54145</td>\n",
       "      <td>0.45</td>\n",
       "      <td>53936</td>\n",
       "      <td>0.565631</td>\n",
       "      <td>1.256958</td>\n",
       "      <td>0.055293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>32575</td>\n",
       "      <td>0.90</td>\n",
       "      <td>32366</td>\n",
       "      <td>1.076321</td>\n",
       "      <td>1.195912</td>\n",
       "      <td>-0.005753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>18100</td>\n",
       "      <td>1.35</td>\n",
       "      <td>17891</td>\n",
       "      <td>1.669132</td>\n",
       "      <td>1.236394</td>\n",
       "      <td>0.034729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>10354</td>\n",
       "      <td>1.80</td>\n",
       "      <td>10145</td>\n",
       "      <td>2.236448</td>\n",
       "      <td>1.242471</td>\n",
       "      <td>0.040806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6213</td>\n",
       "      <td>2.25</td>\n",
       "      <td>6004</td>\n",
       "      <td>2.761004</td>\n",
       "      <td>1.227113</td>\n",
       "      <td>0.025448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4185</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3976</td>\n",
       "      <td>3.173153</td>\n",
       "      <td>1.175242</td>\n",
       "      <td>-0.026423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2504</td>\n",
       "      <td>3.15</td>\n",
       "      <td>2295</td>\n",
       "      <td>3.722697</td>\n",
       "      <td>1.181808</td>\n",
       "      <td>-0.019857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1666</td>\n",
       "      <td>3.60</td>\n",
       "      <td>1457</td>\n",
       "      <td>4.177050</td>\n",
       "      <td>1.160292</td>\n",
       "      <td>-0.041373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1152</td>\n",
       "      <td>4.05</td>\n",
       "      <td>943</td>\n",
       "      <td>4.612118</td>\n",
       "      <td>1.138795</td>\n",
       "      <td>-0.062870</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$  $\\delta \\mu$\n",
       "1      54145       0.45       53936  0.565631  1.256958      0.055293\n",
       "2      32575       0.90       32366  1.076321  1.195912     -0.005753\n",
       "3      18100       1.35       17891  1.669132  1.236394      0.034729\n",
       "4      10354       1.80       10145  2.236448  1.242471      0.040806\n",
       "5       6213       2.25        6004  2.761004  1.227113      0.025448\n",
       "6       4185       2.70        3976  3.173153  1.175242     -0.026423\n",
       "7       2504       3.15        2295  3.722697  1.181808     -0.019857\n",
       "8       1666       3.60        1457  4.177050  1.160292     -0.041373\n",
       "9       1152       4.05         943  4.612118  1.138795     -0.062870"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Железо"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>52100</td>\n",
       "      <td>1</td>\n",
       "      <td>51891</td>\n",
       "      <td>0.604284</td>\n",
       "      <td>0.604284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>29492</td>\n",
       "      <td>2</td>\n",
       "      <td>29283</td>\n",
       "      <td>1.176422</td>\n",
       "      <td>0.588211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16494</td>\n",
       "      <td>3</td>\n",
       "      <td>16285</td>\n",
       "      <td>1.763185</td>\n",
       "      <td>0.587728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9744</td>\n",
       "      <td>4</td>\n",
       "      <td>9535</td>\n",
       "      <td>2.298460</td>\n",
       "      <td>0.574615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5342</td>\n",
       "      <td>5</td>\n",
       "      <td>5133</td>\n",
       "      <td>2.917739</td>\n",
       "      <td>0.583548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3562</td>\n",
       "      <td>6</td>\n",
       "      <td>3353</td>\n",
       "      <td>3.343574</td>\n",
       "      <td>0.557262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2273</td>\n",
       "      <td>7</td>\n",
       "      <td>2064</td>\n",
       "      <td>3.828784</td>\n",
       "      <td>0.546969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1358</td>\n",
       "      <td>8</td>\n",
       "      <td>1149</td>\n",
       "      <td>4.414537</td>\n",
       "      <td>0.551817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>879</td>\n",
       "      <td>9</td>\n",
       "      <td>670</td>\n",
       "      <td>4.953907</td>\n",
       "      <td>0.550434</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$\n",
       "1      52100          1       51891  0.604284  0.604284\n",
       "2      29492          2       29283  1.176422  0.588211\n",
       "3      16494          3       16285  1.763185  0.587728\n",
       "4       9744          4        9535  2.298460  0.574615\n",
       "5       5342          5        5133  2.917739  0.583548\n",
       "6       3562          6        3353  3.343574  0.557262\n",
       "7       2273          7        2064  3.828784  0.546969\n",
       "8       1358          8        1149  4.414537  0.551817\n",
       "9        879          9         670  4.953907  0.550434"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fe =  create_table([\n",
    "    52100,\n",
    "    29492,\n",
    "    16494,\n",
    "    9744,\n",
    "    5342,\n",
    "    3562,\n",
    "    2273,\n",
    "    1358,\n",
    "    879],1,N0)\n",
    "fe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu_fe_aver = 0.5716521218463746\n",
      "Cреднеквадратичное отклонение = 0.020638929274498202\n"
     ]
    }
   ],
   "source": [
    "mu_fe_aver = np.mean(fe.iloc[:,4])\n",
    "mu_fe_delta = fe.iloc[:,4] - mu_fe_aver\n",
    "fe['$\\delta \\mu$'] = mu_fe_delta\n",
    "print('mu_fe_aver =',mu_fe_aver)\n",
    "print('Cреднеквадратичное отклонение =',np.std(fe.iloc[:,4], ddof=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\delta \\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>52100</td>\n",
       "      <td>1</td>\n",
       "      <td>51891</td>\n",
       "      <td>0.604284</td>\n",
       "      <td>0.604284</td>\n",
       "      <td>0.032632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>29492</td>\n",
       "      <td>2</td>\n",
       "      <td>29283</td>\n",
       "      <td>1.176422</td>\n",
       "      <td>0.588211</td>\n",
       "      <td>0.016559</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16494</td>\n",
       "      <td>3</td>\n",
       "      <td>16285</td>\n",
       "      <td>1.763185</td>\n",
       "      <td>0.587728</td>\n",
       "      <td>0.016076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9744</td>\n",
       "      <td>4</td>\n",
       "      <td>9535</td>\n",
       "      <td>2.298460</td>\n",
       "      <td>0.574615</td>\n",
       "      <td>0.002963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5342</td>\n",
       "      <td>5</td>\n",
       "      <td>5133</td>\n",
       "      <td>2.917739</td>\n",
       "      <td>0.583548</td>\n",
       "      <td>0.011896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>3562</td>\n",
       "      <td>6</td>\n",
       "      <td>3353</td>\n",
       "      <td>3.343574</td>\n",
       "      <td>0.557262</td>\n",
       "      <td>-0.014390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2273</td>\n",
       "      <td>7</td>\n",
       "      <td>2064</td>\n",
       "      <td>3.828784</td>\n",
       "      <td>0.546969</td>\n",
       "      <td>-0.024683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1358</td>\n",
       "      <td>8</td>\n",
       "      <td>1149</td>\n",
       "      <td>4.414537</td>\n",
       "      <td>0.551817</td>\n",
       "      <td>-0.019835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>879</td>\n",
       "      <td>9</td>\n",
       "      <td>670</td>\n",
       "      <td>4.953907</td>\n",
       "      <td>0.550434</td>\n",
       "      <td>-0.021218</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$  $\\delta \\mu$\n",
       "1      52100          1       51891  0.604284  0.604284      0.032632\n",
       "2      29492          2       29283  1.176422  0.588211      0.016559\n",
       "3      16494          3       16285  1.763185  0.587728      0.016076\n",
       "4       9744          4        9535  2.298460  0.574615      0.002963\n",
       "5       5342          5        5133  2.917739  0.583548      0.011896\n",
       "6       3562          6        3353  3.343574  0.557262     -0.014390\n",
       "7       2273          7        2064  3.828784  0.546969     -0.024683\n",
       "8       1358          8        1149  4.414537  0.551817     -0.019835\n",
       "9        879          9         670  4.953907  0.550434     -0.021218"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "hide_input": true,
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "all_cof = fit(all.iloc[:,1],all.iloc[:,3])\n",
    "pb_cof = fit(pb.iloc[:,1],pb.iloc[:,3])\n",
    "fe_cof = fit(fe.iloc[:,1],fe.iloc[:,3])\n",
    "cof = [all_cof,pb_cof,fe_cof]\n",
    "all_x = np.linspace(min(all.iloc[:,1]),max(all.iloc[:,1]),100)\n",
    "pb_x = np.linspace(min(pb.iloc[:,1]),max(pb.iloc[:,1]),100)\n",
    "fe_x = np.linspace(min(fe.iloc[:,1]),max(fe.iloc[:,1]),100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "jupyter": {
     "source_hidden": true
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   },
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       "                        {\"responsive\": true}\n",
       "                    ).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('7fad2e4e-9cfd-4b09-856e-52db66fd50f5');\n",
       "var x = new MutationObserver(function (mutations, observer) {{\n",
       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
       "            observer.disconnect();\n",
       "        }}\n",
       "}});\n",
       "\n",
       "// Listen for the removal of the full notebook cells\n",
       "var notebookContainer = gd.closest('#notebook-container');\n",
       "if (notebookContainer) {{\n",
       "    x.observe(notebookContainer, {childList: true});\n",
       "}}\n",
       "\n",
       "// Listen for the clearing of the current output cell\n",
       "var outputEl = gd.closest('.output');\n",
       "if (outputEl) {{\n",
       "    x.observe(outputEl, {childList: true});\n",
       "}}\n",
       "\n",
       "                        })\n",
       "                };\n",
       "                });\n",
       "            </script>\n",
       "        </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = go.Figure()\n",
    "fig.add_trace(go.Scatter(x = all.iloc[:,1],y=all.iloc[:,3],\n",
    "                    mode='markers',\n",
    "                             marker=dict(color='red'),\n",
    "                         error_y=dict(\n",
    "                            type='constant',\n",
    "                            value=np.std(all.iloc[:,4], ddof=1)),\n",
    "                    name='Аллюминий'))\n",
    "fig.add_trace(go.Scatter(x = all_x,y=all_x*all_cof[0]+all_cof[1],\n",
    "                             line=dict(color='red'),showlegend=False))\n",
    "              \n",
    "fig.add_trace(go.Scatter(x = pb.iloc[:,1],y=pb.iloc[:,3],\n",
    "                    mode='markers',\n",
    "                             marker=dict(color='green'),\n",
    "                         error_y=dict(\n",
    "                            type='constant',\n",
    "                            value=np.std(pb.iloc[:,4], ddof=1)),\n",
    "                    name='Свинец'))\n",
    "\n",
    "fig.add_trace(go.Scatter(x = pb_x,y=pb_x*pb_cof[0]+pb_cof[1],\n",
    "                             line=dict(color='green'),showlegend=False))\n",
    "              \n",
    "fig.add_trace(go.Scatter(x = fe.iloc[:,1],y=fe.iloc[:,3],\n",
    "                    mode='markers',\n",
    "                             marker=dict(color='blue'),\n",
    "                         error_y=dict(\n",
    "                            type='constant',\n",
    "                            value=np.std(fe.iloc[:,4], ddof=1)),\n",
    "                    name='Железо'))\n",
    "fig.add_trace(go.Scatter(x = fe_x,y=fe_x*fe_cof[0]+fe_cof[1],\n",
    "                             line=dict(color='blue'),showlegend=False))\n",
    "fig.update_layout( xaxis_title='Длина(cm)',\n",
    "                   yaxis_title='ln(N)')\n",
    "fig.show()\n",
    "#fig.write_image(\"images/fig1.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N с шумом</th>\n",
       "      <th>Длина(cm)</th>\n",
       "      <th>N без шума</th>\n",
       "      <th>ln(N)</th>\n",
       "      <th>$\\mu$</th>\n",
       "      <th>$\\delta \\mu$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>61200</td>\n",
       "      <td>2</td>\n",
       "      <td>60991</td>\n",
       "      <td>0.442703</td>\n",
       "      <td>0.221352</td>\n",
       "      <td>0.013053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>41053</td>\n",
       "      <td>4</td>\n",
       "      <td>40844</td>\n",
       "      <td>0.843669</td>\n",
       "      <td>0.210917</td>\n",
       "      <td>0.002619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>27267</td>\n",
       "      <td>6</td>\n",
       "      <td>27058</td>\n",
       "      <td>1.255447</td>\n",
       "      <td>0.209241</td>\n",
       "      <td>0.000943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>18350</td>\n",
       "      <td>8</td>\n",
       "      <td>18141</td>\n",
       "      <td>1.655255</td>\n",
       "      <td>0.206907</td>\n",
       "      <td>-0.001391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12489</td>\n",
       "      <td>10</td>\n",
       "      <td>12280</td>\n",
       "      <td>2.045458</td>\n",
       "      <td>0.204546</td>\n",
       "      <td>-0.003752</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>8583</td>\n",
       "      <td>12</td>\n",
       "      <td>8374</td>\n",
       "      <td>2.428298</td>\n",
       "      <td>0.202358</td>\n",
       "      <td>-0.005940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5764</td>\n",
       "      <td>14</td>\n",
       "      <td>5555</td>\n",
       "      <td>2.838731</td>\n",
       "      <td>0.202766</td>\n",
       "      <td>-0.005532</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   N с шумом  Длина(cm)  N без шума     ln(N)     $\\mu$  $\\delta \\mu$\n",
       "1      61200          2       60991  0.442703  0.221352      0.013053\n",
       "2      41053          4       40844  0.843669  0.210917      0.002619\n",
       "3      27267          6       27058  1.255447  0.209241      0.000943\n",
       "4      18350          8       18141  1.655255  0.206907     -0.001391\n",
       "5      12489         10       12280  2.045458  0.204546     -0.003752\n",
       "6       8583         12        8374  2.428298  0.202358     -0.005940\n",
       "7       5764         14        5555  2.838731  0.202766     -0.005532"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ln(N/N0)/l Аллюминий = 0.199\n",
      "Ln(N/N0)/l Свинец = 1.131\n",
      "Ln(N/N0)/l Железо = 0.538\n"
     ]
    }
   ],
   "source": [
    "mat = ['Аллюминий','Свинец','Железо']\n",
    "for i in range(3):\n",
    "    print('Ln(N/N0)/l',mat[i],'=',round(cof[i][0],3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ln(N/N0)/l Аллюминий = 0.0737037037037037\n",
      "Ln(N/N0)/l Свинец = 0.09973544973544973\n",
      "Ln(N/N0)/l Железо = 0.06832613665227331\n"
     ]
    }
   ],
   "source": [
    "mat_ro = [2.7, 11.34, 7.874]\n",
    "for i in range(3):\n",
    "    print('Ln(N/N0)/l',mat[i],'=',round(cof[i][0],3)/ mat_ro[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "cell_style": "center"
   },
   "outputs": [],
   "source": []
  }
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