{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# M1.D1: Bohr's hydrogen atom\n",
    "\n",
    "## Learning Objectives\n",
    "\n",
    "* Use loops in Python using Bohr's equation to calculate the first ten energy levels of hydrogen\n",
    "* Use matplotlib to plot the electronic levels of hydrogen in the logorithmic scale\n",
    "* Use loops in Python to calculate the wavelengths in nm for the first ten emissions of the Lyman series\n",
    "* Use matplotlib to plot the emission spectrum of the Lyman series\n",
    "* Repeat the same exercise for the Balmer and Paschen series\n",
    "* Use frequency in Hz instead of wavelength to plot the three Hydrogen emission series\n",
    "\n",
    "**Context and goals**\n",
    "Before we discuss all the energy levels in atoms and molecules it may be interesting to discuss that scientists already knew that matter emitted certain values of light not a continuum. Explaining the spectral series of Hydrogen was a fundamental step towards the development of quantum theory for atoms and molecules.\n",
    "Our goal today is to try to reproduce with Python the experimental spectral series of hydrogen.\n",
    "\n",
    "# Experimental Spectral Series\n",
    "\n",
    "For a long time scientists knew that the light that was coming out of hydrogen could be wrapped in series.\n",
    "\n",
    "* Lyman's series (nf = 1)\n",
    "* Balmer's series (nf = 2)\n",
    "* Paschen's series (nf = 3)\n",
    "* Bracket's series (nf = 4)\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/4/41/Hydrogen_spectrum.svg\"/>\n",
    "\n",
    "Out of these series, only the Balmber series is visible \n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/6/60/Emission_spectrum-H.svg\" />\n",
    "\n",
    "There were even experimental equations to explain those lines and predict the wavelength of emission. The Rydeberg equation\n",
    "\n",
    "$$\n",
    "\\frac{1}{\\lambda} = R \\left( \\frac{1}{n_f^{2}} - \\frac{1}{n_i^{2}} \\right)\n",
    "$$\n",
    "\n",
    "Where $R = 1.09677583×10^{7} m^{−1}$\n",
    "\n",
    "\n",
    "\n",
    "# Bohr's hydrogen model\n",
    "\n",
    "Neils Bohr came up with they hypothesis that the electron \"orbits\" around the nucleus at a given and fixed energy level. For the original paper see <a href=\"https://link.springer.com/chapter/10.1007%2F978-3-319-14316-3_2\">here</a>\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/b/b2/Hydrogen_transitions.svg\"/>\n",
    "\n",
    "The energy of the orbit depends on the quantum number $n = 1,2,3,4...$\n",
    "\n",
    "$$ E_n = \\frac{-13.6 eV}{n^{2}}\n",
    "$$\n",
    "\n",
    "Notice that the above equation is in electron Volts. That is, the unit of energy that one electron has in a 1 Volt poential: $q_{e^{-}} = 1.6*10^{-19} Coulombs $; $E=q*V$\n",
    "\n",
    "$$\\frac{  m_e e^4}{2 ( 4 \\pi \\varepsilon_0)^2 \\hbar^2 } =\\frac{m_{\\text{e}} e^4}{8 h^2 \\varepsilon_0^2}= 1 \\,\\text{Ry} = 13.605\\;693\\;122\\;994(26) \\,\\text{eV}$$\n",
    "\n",
    "**Lets do some Python**\n",
    "\n",
    "The levels can be calculated with a loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-13.605693122994, -3.4014232807485, -1.5117436803326667, -0.850355820187125, -0.54422772491976, -0.3779359200831667, -0.2776672065917143, -0.21258895504678124, -0.16797152003696295, -0.13605693122994]\n"
     ]
    }
   ],
   "source": [
    "#lets get the energy levels using Bohr's equation\n",
    "\n",
    "levels = []\n",
    "numberLevels = 10\n",
    "eV = 13.605693122994\n",
    "for n in range(1,numberLevels+1):\n",
    "    ene = -(eV/n**2)\n",
    "    levels.append(ene)\n",
    "    \n",
    "print(levels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Exercise"
    ]
   },
   "source": [
    "**Your turn**: \n",
    "\n",
    "write a loop to print the first twenty levels of the hydrogen atom\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The levels can be graphically displayed in a plot (notice that the x-axis does not have any physical meaning)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variable numberLevels is =  10  and the number of levels computed is  10\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "print(\"The variable numberLevels is = \",numberLevels,\" and the number of levels computed is \",len(levels))\n",
    "x = [1]*numberLevels #all points in the x axis will have a value of 1 so that they are in vertical order\n",
    "y = levels #the levels is the list of energies computer in the previous cells\n",
    "plt.scatter(x, y,marker = \"_\",s=10000) #s is the marker size, we make it big (1000) to see it\n",
    "plt.title(\"Electronic energy levels of hydrogen. E(eV)\")\n",
    "plt.ylabel(\"Energy (eV)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Exercise"
    ]
   },
   "source": [
    "**Your turn**\n",
    "* Notice that the previous code starts with \"import\". What does that do?\n",
    "* Notice that the previous code has the \"#\" sign. What does that do?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logarithmic scale\n",
    "\n",
    "As you can see higher energy levels merge very easily. We can use a logarithmic scale to see more levels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variable numberLevels is =  10  and the number of levels computed is  10\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "print(\"The variable numberLevels is = \",numberLevels,\" and the number of levels computed is \",len(levels))\n",
    "loglevels = []\n",
    "for n in range(1,numberLevels+1):\n",
    "    ene = (eV/n**2)\n",
    "    logene = -math.log(ene)\n",
    "    #print(ene,logene)\n",
    "    loglevels.append(logene)\n",
    "    \n",
    "x = [1]*numberLevels\n",
    "y = loglevels\n",
    "plt.scatter(x, y,marker = \"_\",s=1000)\n",
    "\n",
    "plt.title(\"Electronic energy levels of hydrogen. E(log(eV))\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Exercise"
    ]
   },
   "source": [
    "* Why in the logarithmic scale some energies are negative and others are positive?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculating wavelengths of the Lyman series\n",
    "\n",
    "Since we know the energy of each electronic level, we can calculate the energy difference between levels and convert the energy into wavelength of the photon involved.\n",
    "\n",
    "* We need to convert the units of energy eV into joules knowing that $1.6x10^{-19} J = 1 eV$\n",
    "* Remember that the speed of light relate the wavelength (in meters) with the frequency (in $s^{-1}$) of the photon\n",
    "\n",
    "$$ c = \\lambda *\\nu$$ \n",
    "$$E = h*\\nu = \\frac{h*c}{\\lambda} ; \\lambda = \\frac{h*c}{E}$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The energy difference between level 2 and level 1  is = 1.6349042565416829e-18 J. And Lamda= 121.5022724556172 nm\n",
      "The energy difference between level 3 and level 1  is = 1.937664304049402e-18 J. And Lamda= 102.51754238442699 nm\n",
      "The energy difference between level 4 and level 1  is = 2.0436303206771033e-18 J. And Lamda= 97.20181796449377 nm\n",
      "The energy difference between level 5 and level 1  is = 2.0926774483733542e-18 J. And Lamda= 94.92365035595093 nm\n",
      "The energy difference between level 6 and level 1  is = 2.1193203325540334e-18 J. And Lamda= 93.73032446576184 nm\n",
      "The energy difference between level 7 and level 1  is = 2.1353851514013818e-18 J. And Lamda= 93.0251773488319 nm\n",
      "The energy difference between level 8 and level 1  is = 2.145811836710959e-18 J. And Lamda= 92.57315996618453 nm\n",
      "The energy difference between level 9 and level 1  is = 2.152960337832669e-18 J. And Lamda= 92.2657881459843 nm\n",
      "The energy difference between level 10 and level 1  is = 2.1580736186350215e-18 J. And Lamda= 92.04717610274028 nm\n",
      "[121.5022724556172, 102.51754238442699, 97.20181796449377, 94.92365035595093, 93.73032446576184, 93.0251773488319, 92.57315996618453, 92.2657881459843, 92.04717610274028]\n"
     ]
    }
   ],
   "source": [
    "#now let's see what the spectrum looks like\n",
    "\n",
    "#constants\n",
    "c = 299792458 \n",
    "h = 6.62607004*10**(-34)\n",
    "qe = 1.60217662*10**(-19)\n",
    "\n",
    "nf = 1 #Calculating the Lyman series, so the final level is always 1 \n",
    "wavelengths = []\n",
    "for ni in range(nf+1,numberLevels+1):\n",
    "    #the emission process is exothermic, so it's negative, let's make it positive for getting the wavelengths\n",
    "    energy_difference = -(levels[nf-1] - levels[ni-1])*qe\n",
    "    lamda = (c*h/energy_difference)*10**9\n",
    "    print(\"The energy difference between level\",ni, \"and level\",nf,\" is =\",energy_difference,\"J. And Lamda=\",lamda,\"nm\")\n",
    "    wavelengths.append(lamda)\n",
    "    \n",
    "print(wavelengths)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Exercise"
    ]
   },
   "source": [
    "* Find in the code where the energy is converted from eV to Joules.\n",
    "* Find in the code where the wavelength is converted into nanometers.\n",
    "* At what wavelength does the Lyman series converge? Why does it converge?\n",
    "* To view the wavelengths of the Balmer series you only need to change one value above. Which one is it? At what value of wavelength does the Balmer series converge?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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27dpJOnEvQG3r2bOnJk6cqHHjxqlTp0768ccfNWHCBMXGxqq0tLTWjtOuXTv17NlT1113nS699FJt375dCxYsUPv27VWvXj1JJ37YJiUlqVu3burfv78uu+wyHThwQNu3b9fGjRv1zjvvuHzc6n6dCgoK1KVLF/Xp00dXX3216tevr3Xr1mnZsmUOMzUTJkzQhAkT9MUXXzjMWlSlS5cumjx5smw2m5577jmHdZ06ddILL7wgy7Ls98pIUocOHXTppZcqNTVV48aNk7e3txYuXKgtW7ZUeoyrr75a7du3V0ZGhnJycvTqq6/WaAzOZvxcceuttyohIUEjRoxQYWGh4uLitGbNGs2fP1+S5OHxf7cHtmjRQpL073//W/369ZO3t7eaNm3q0oPL2rVrJ39/f61du9bpfpbzbe3atTzYrg4gjOCCcv/996tRo0aaNGmSHnroIR0+fFgNGzZUq1at1L9//2rtY/78+fZvwiebO3eu+vfvr7Zt2+qKK66Qv7+/brrpplp+B9LYsWN19OhRzZ49W5MmTdI111yjmTNnasmSJZV+tLemunbtqg8//FAvvPCCjh49qssuu0x9+/bV2LFj7X26dOmib775Rv/zP/+jYcOG6eDBg2rQoIGuueYap5sdXVGdr5Ofn5/atWunBQsW6LffflNJSYkaNWqkUaNG6Z///Kd9X+Xl5SorK6v2RzMrwoiHh4f9PpEKHTt2lM1mk2VZ9htbpROXMT755BONGDFC999/vwICAnT77bcrMzPT4WOtJxswYID+/ve/y9/f3+kG5+qOwdmMnys8PDz00UcfacSIEXr22Wd1/PhxJSQk6I033tANN9zg8CyQzp07Kz09Xa+//rpee+01lZeXa/ny5Q7jdSY+Pj66++679cEHH9TqrJurjhw5oi+++EITJ040VgNqh82q7ncAoI749ttv1bJlS7388st6+OGHTZcDnDNvvvmm7rvvPn399de1/oTS9evX6/rrr9fatWvtM43n2+zZs/XYY48pJyeHmRE3RxjBRePXX3/Vrl27NGbMGGVnZ+uXX36xX84A3N2iRYu0Z88etWjRQh4eHlq7dq0mT56s1q1bn7Pf3ZKSkqKioiKnp6ueD6WlpbrmmmvUr18/h9lAuCeeM4KLxsSJE3XLLbfoyJEjeueddwgiqFPq16+vt956SykpKerevbtee+019e/fXx999NE5O+bzzz+v66+/3shv7c3JydH999/P7x6qI5gZAQAARjEzAgAAjCKMAAAAowgjAADAKLd4zkh5ebn27t2r+vXrV+tx1QAAwDzLsnT48GFFRUU5PHzvVG4RRvbu3XvOHqMNAADOrZycHF1++eVVrneLMFLxmOKcnBwFBQUZrgYAAFRHYWGhoqOjz/jrBtwijFRcmgkKCiKMAADgZs50iwU3sAIAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAol8PIl19+qeTkZEVFRclms+n9998/4zYrV65UXFyc/Pz8dOWVV2rmzJk1qRUAANRBLoeRoqIitWzZUtOmTatW/507d6p79+7q2LGjNm3apDFjxmjo0KF67733XC4WAADUPS7/orykpCQlJSVVu//MmTPVqFEjTZ06VZLUrFkzrV+/Xv/617901113VbpNcXGxiouL7cuFhYWulgkAANzEOb9nZM2aNUpMTHRo69atm9avX6+SkpJKt8nIyFBwcLD9FR0dXfuFFRVJNtuJV1HRmZdPt60rx6mtek26kGpxZ4wjANMukO9D5zyM5OXlKTw83KEtPDxcpaWl2r9/f6XbpKenq6CgwP7Kyck512UCAABDXL5MUxM2m81h2bKsStsr+Pr6ytfX95zXBQAAzDvnMyMRERHKy8tzaNu3b5+8vLzUoEGDc314AABwgTvnYaR9+/bKyspyaPvss88UHx8vb2/vc314AABwgXM5jBw5ckSbN2/W5s2bJZ346O7mzZuVnZ0t6cT9Hn379rX3T01N1a5du5SWlqbt27drzpw5mj17tkaOHFk77wAAALg1l+8ZWb9+vbp06WJfTktLkyT169dP8+bNU25urj2YSFJsbKyWLl2q4cOH6+WXX1ZUVJRefPHFKj/WCwAALi4uh5HOnTvbb0CtzLx585zaOnXqpI0bN7p6KAAAcBHgd9MAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjKpRGJk+fbpiY2Pl5+enuLg4rVq16rT9Fy5cqJYtW6pevXqKjIzUgAEDlJ+fX6OCAQBA3eJyGMnMzNSwYcM0duxYbdq0SR07dlRSUpKys7Mr7f/VV1+pb9++GjRokL7//nu98847WrdunQYPHnzWxQMAAPfnchiZMmWKBg0apMGDB6tZs2aaOnWqoqOjNWPGjEr7r127VldccYWGDh2q2NhY3XjjjXrooYe0fv36sy4eAAC4P5fCyPHjx7VhwwYlJiY6tCcmJmr16tWVbtOhQwft3r1bS5culWVZ+v333/Xuu++qR48eVR6nuLhYhYWFDi8AAFA3uRRG9u/fr7KyMoWHhzu0h4eHKy8vr9JtOnTooIULFyolJUU+Pj6KiIjQJZdcopdeeqnK42RkZCg4ONj+io6OdqVMAADgRmp0A6vNZnNYtizLqa3Ctm3bNHToUD355JPasGGDli1bpp07dyo1NbXK/aenp6ugoMD+ysnJqUmZAADADXi50jk0NFSenp5OsyD79u1zmi2pkJGRoYSEBD3++OOSpOuuu04BAQHq2LGjnn76aUVGRjpt4+vrK19fX1dKAwAAbsqlmREfHx/FxcUpKyvLoT0rK0sdOnSodJujR4/Kw8PxMJ6enpJOzKgAAICLm8uXadLS0jRr1izNmTNH27dv1/Dhw5WdnW2/7JKenq6+ffva+ycnJ2vx4sWaMWOGduzYoa+//lpDhw5V27ZtFRUVVXvvBAAAuCWXLtNIUkpKivLz8zVhwgTl5uaqefPmWrp0qWJiYiRJubm5Ds8c6d+/vw4fPqxp06ZpxIgRuuSSS9S1a1c999xztfcuAACA27JZbnCtpLCwUMHBwSooKFBQUFDt7LSoSAoMPPH3I0dO/Hm65YCAqrc9ed2ZjnO6vq7UW9P91IYLqRZ3xjgCMO0cfx+q7s9vfjcNAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwKgahZHp06crNjZWfn5+iouL06pVq07bv7i4WGPHjlVMTIx8fX111VVXac6cOTUqGAAA1C1erm6QmZmpYcOGafr06UpISNArr7yipKQkbdu2TY0aNap0m969e+v333/X7Nmz9Ze//EX79u1TaWnpWRcPAADcn8thZMqUKRo0aJAGDx4sSZo6dao+/fRTzZgxQxkZGU79ly1bppUrV2rHjh0KCQmRJF1xxRVnVzUAAKgzXLpMc/z4cW3YsEGJiYkO7YmJiVq9enWl23z44YeKj4/XpEmTdNlll6lJkyYaOXKkjh07VuVxiouLVVhY6PACAAB1k0szI/v371dZWZnCw8Md2sPDw5WXl1fpNjt27NBXX30lPz8/LVmyRPv379fDDz+sAwcOVHnfSEZGhp566ilXSgMAAG6qRjew2mw2h2XLspzaKpSXl8tms2nhwoVq27atunfvrilTpmjevHlVzo6kp6eroKDA/srJyalJmQAAwA24NDMSGhoqT09Pp1mQffv2Oc2WVIiMjNRll12m4OBge1uzZs1kWZZ2796txo0bO23j6+srX19fV0oDAABuyqWZER8fH8XFxSkrK8uhPSsrSx06dKh0m4SEBO3du1dHjhyxt/3000/y8PDQ5ZdfXoOSAQBAXeLyZZq0tDTNmjVLc+bM0fbt2zV8+HBlZ2crNTVV0olLLH379rX379Onjxo0aKABAwZo27Zt+vLLL/X4449r4MCB8vf3r713AgAA3JLLH+1NSUlRfn6+JkyYoNzcXDVv3lxLly5VTEyMJCk3N1fZ2dn2/oGBgcrKytKjjz6q+Ph4NWjQQL1799bTTz9de+8CAAC4LZtlWZbpIs6ksLBQwcHBKigoUFBQUO3stKhICgw88feKS0inWw4IqHrbk9ed6Tin6+tKvTXdT224kGpxZ4wjANPO8feh6v785nfTAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIyqURiZPn26YmNj5efnp7i4OK1atapa23399dfy8vJSq1atanJYAABQB7kcRjIzMzVs2DCNHTtWmzZtUseOHZWUlKTs7OzTbldQUKC+ffvqpptuqnGxAACg7nE5jEyZMkWDBg3S4MGD1axZM02dOlXR0dGaMWPGabd76KGH1KdPH7Vv377GxQIAgLrHpTBy/PhxbdiwQYmJiQ7tiYmJWr16dZXbzZ07V7/++qvGjRtXreMUFxersLDQ4QUAAOoml8LI/v37VVZWpvDwcIf28PBw5eXlVbrNzz//rNGjR2vhwoXy8vKq1nEyMjIUHBxsf0VHR7tSJgAAcCM1uoHVZrM5LFuW5dQmSWVlZerTp4+eeuopNWnSpNr7T09PV0FBgf2Vk5NTkzIBAIAbqN5Uxf8XGhoqT09Pp1mQffv2Oc2WSNLhw4e1fv16bdq0SUOGDJEklZeXy7IseXl56bPPPlPXrl2dtvP19ZWvr68rpQEAADfl0syIj4+P4uLilJWV5dCelZWlDh06OPUPCgrS1q1btXnzZvsrNTVVTZs21ebNm9WuXbuzqx4AALg9l2ZGJCktLU0PPPCA4uPj1b59e7366qvKzs5WamqqpBOXWPbs2aP58+fLw8NDzZs3d9i+YcOG8vPzc2oHAAAXJ5fDSEpKivLz8zVhwgTl5uaqefPmWrp0qWJiYiRJubm5Z3zmCAAAQAWbZVmW6SLOpLCwUMHBwSooKFBQUFDt7LSoSAoMPPH3I0dO/Hm65YCAqrc9ed2ZjnO6vq7UW9P91IYLqRZ3xjgCMO0cfx+q7s9vfjcNAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjAADAKMIIAAAwijACAACMIowAAACjCCMAAMAowggAADCKMAIAAIwijAAAAKMIIwAAwKgahZHp06crNjZWfn5+iouL06pVq6rsu3jxYt1yyy0KCwtTUFCQ2rdvr08//bTGBQMAgLrF5TCSmZmpYcOGaezYsdq0aZM6duyopKQkZWdnV9r/yy+/1C233KKlS5dqw4YN6tKli5KTk7Vp06azLh4AALg/m2VZlisbtGvXTm3atNGMGTPsbc2aNdMdd9yhjIyMau3j2muvVUpKip588slq9S8sLFRwcLAKCgoUFBTkSrlVKyqSAgNP/P3IkRN/nm45IKDqbU9ed6bjnK6vK/XWdD+14UKqxZ0xjgBMO8ffh6r789ulmZHjx49rw4YNSkxMdGhPTEzU6tWrq7WP8vJyHT58WCEhIVX2KS4uVmFhocMLAADUTS6Fkf3796usrEzh4eEO7eHh4crLy6vWPp5//nkVFRWpd+/eVfbJyMhQcHCw/RUdHe1KmQAAwI3U6AZWm83msGxZllNbZRYtWqTx48crMzNTDRs2rLJfenq6CgoK7K+cnJyalAkAANyAlyudQ0ND5enp6TQLsm/fPqfZklNlZmZq0KBBeuedd3TzzTeftq+vr698fX1dKQ0AALgpl2ZGfHx8FBcXp6ysLIf2rKwsdejQocrtFi1apP79++vNN99Ujx49alYpAACok1yaGZGktLQ0PfDAA4qPj1f79u316quvKjs7W6mpqZJOXGLZs2eP5s+fL+lEEOnbt6/+/e9/64YbbrDPqvj7+ys4OLgW3woAAHBHLoeRlJQU5efna8KECcrNzVXz5s21dOlSxcTESJJyc3MdnjnyyiuvqLS0VI888ogeeeQRe3u/fv00b968s38HAADArbn8nBETeM5ILe6nNlxItbgzxhGAae74nBEAAIDaRhgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABGEUYAAIBRhBEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGFWjMDJ9+nTFxsbKz89PcXFxWrVq1Wn7r1y5UnFxcfLz89OVV16pmTNn1qhYAABQ93i5ukFmZqaGDRum6dOnKyEhQa+88oqSkpK0bds2NWrUyKn/zp071b17dz344IN644039PXXX+vhhx9WWFiY7rrrrlp5EzVhWZYsm+3EwrFjJ/483XLF309dPnXdqVzpezq1tZ/acCHV4s4YRwCmnfS9x2ZZMvVdyGZZluXKBu3atVObNm00Y8YMe1uzZs10xx13KCMjw6n/qFGj9OGHH2r79u32ttTUVG3ZskVr1qyp9BjFxcUqLi62LxcWFio6OloFBQUKCgpypdwqle/frx9v7Fgr+wIAwN01/WqVPEJDa3WfhYWFCg4OPuPPb5cu0xw/flwbNmxQYmKiQ3tiYqJWr15d6TZr1qxx6t+tWzetX79eJSUllW6TkZGh4OBg+ys6OtqVMqunXr3a3ycAAO7K4M9Fly7T7N+/X2VlZQoPD3doDw8PV15eXqXb5OXlVdq/tLRU+/fvV2RkpNM26enpSktLsy9XzIzUJpu/v5pu3FCr+wQAwF3Z/P2NHdvle0YkyXbKtW3LspzaztS/svYKvr6+8vX1rUlp1Waz2WRjdgQAAONcukwTGhoqT09Pp1mQffv2Oc1+VIiIiKi0v5eXlxo0aOBiuQAAoK5xKYz4+PgoLi5OWVlZDu1ZWVnq0KFDpdu0b9/eqf9nn32m+Ph4eXt7u1guAACoa1x+zkhaWppmzZqlOXPmaPv27Ro+fLiys7OVmpoq6cT9Hn379rX3T01N1a5du5SWlqbt27drzpw5mj17tkaOHFl77wIAALgtl+8ZSUlJUX5+viZMmKDc3Fw1b95cS5cuVUxMjCQpNzdX2dnZ9v6xsbFaunSphg8frpdffllRUVF68cUXjT5jBAAAXDhcfs6ICdX9nDIAALhwnJPnjAAAANQ2wggAADCKMAIAAIwijAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAo2r0W3vPt4rnshUWFhquBAAAVFfFz+0zPV/VLcLI4cOHJUnR0dGGKwEAAK46fPiwgoODq1zvFo+DLy8v1969e1W/fn3ZbDbT5RhXWFio6Oho5eTk8Hj8amC8XMeYuYbxch1j5hp3HS/LsnT48GFFRUXJw6PqO0PcYmbEw8NDl19+uekyLjhBQUFudVKaxni5jjFzDePlOsbMNe44XqebEanADawAAMAowggAADCKMOKGfH19NW7cOPn6+pouxS0wXq5jzFzDeLmOMXNNXR8vt7iBFQAA1F3MjAAAAKMIIwAAwCjCCAAAMIowAgAAjCKMAAAAowgjF7DDhw9r2LBhiomJkb+/vzp06KB169bZ1/fv3182m83hdcMNNxis+Pz58ssvlZycrKioKNlsNr3//vsO6y3L0vjx4xUVFSV/f3917txZ33//vUOf4uJiPfroowoNDVVAQIBuu+027d69+zy+i/OrNsasc+fOTufc3/72t/P4Ls6fM43X4sWL1a1bN4WGhspms2nz5s1O++Ace99hfXXG7GI6x6TTj1lJSYlGjRqlFi1aKCAgQFFRUerbt6/27t3rsI+6cJ4RRi5ggwcPVlZWlhYsWKCtW7cqMTFRN998s/bs2WPvc+uttyo3N9f+Wrp0qcGKz5+ioiK1bNlS06ZNq3T9pEmTNGXKFE2bNk3r1q1TRESEbrnlFvsvXZSkYcOGacmSJXrrrbf01Vdf6ciRI+rZs6fKysrO19s4r2pjzCTpwQcfdDjnXnnllfNR/nl3pvEqKipSQkKCnn322Sr3wTnmvP5MYyZdPOeYdPoxO3r0qDZu3KgnnnhCGzdu1OLFi/XTTz/ptttuc+hXJ84zCxeko0ePWp6entbHH3/s0N6yZUtr7NixlmVZVr9+/azbb7/dQHUXFknWkiVL7Mvl5eVWRESE9eyzz9rb/vzzTys4ONiaOXOmZVmWdejQIcvb29t666237H327NljeXh4WMuWLTtvtZtSkzGzLMvq1KmT9dhjj53HSi8Mp47XyXbu3GlJsjZt2uTQzjnm+phZ1sV7jlnW6ceswjfffGNJsnbt2mVZVt05z5gZuUCVlpaqrKxMfn5+Du3+/v766quv7MsrVqxQw4YN1aRJEz344IPat2/f+S71grNz507l5eUpMTHR3ubr66tOnTpp9erVkqQNGzaopKTEoU9UVJSaN29u73Mxqc6YVVi4cKFCQ0N17bXXauTIkU4zJziBc6zmOMeqVlBQIJvNpksuuURS3TnP3OK39l6M6tevr/bt22vixIlq1qyZwsPDtWjRIv3v//6vGjduLElKSkrSPffco5iYGO3cuVNPPPGEunbtqg0bNtTZRwZXR15eniQpPDzcoT08PFy7du2y9/Hx8dGll17q1Kdi+4tJdcZMku677z7FxsYqIiJC3333ndLT07VlyxZlZWWd13rdAedYzXCOVe3PP//U6NGj1adPH/tv7q0r5xlh5AK2YMECDRw4UJdddpk8PT3Vpk0b9enTRxs3bpQkpaSk2Ps2b95c8fHxiomJ0SeffKJevXqZKvuCYbPZHJYty3JqO1V1+tRlZxqzBx980P735s2bq3HjxoqPj9fGjRvVpk2b81anO7vYz7Ez4RyrXElJif72t7+pvLxc06dPP2N/dzvPuExzAbvqqqu0cuVKHTlyRDk5Ofrmm29UUlKi2NjYSvtHRkYqJiZGP//883mu9MISEREhSU7/K9i3b5/9f/4RERE6fvy4Dh48WGWfi0l1xqwybdq0kbe390V/zlWGc6x2cI6dCCK9e/fWzp07lZWVZZ8VkerOeUYYcQMBAQGKjIzUwYMH9emnn+r222+vtF9+fr5ycnIUGRl5niu8sFRM8Z48rXv8+HGtXLlSHTp0kCTFxcXJ29vboU9ubq6+++47e5+LSXXGrDLff/+9SkpKLvpzrjKcY7XjYj/HKoLIzz//rM8//1wNGjRwWF9XzjMu01zAPv30U1mWpaZNm+qXX37R448/rqZNm2rAgAE6cuSIxo8fr7vuukuRkZH67bffNGbMGIWGhurOO+80Xfo5d+TIEf3yyy/25Z07d2rz5s0KCQlRo0aNNGzYMD3zzDNq3LixGjdurGeeeUb16tVTnz59JEnBwcEaNGiQRowYoQYNGigkJEQjR45UixYtdPPNN5t6W+fU2Y7Zr7/+qoULF6p79+4KDQ3Vtm3bNGLECLVu3VoJCQmm3tY5c6bxOnDggLKzs+3PfPjxxx8lnfifakREBOeYXB+zi+0ck04/ZlFRUbr77ru1ceNGffzxxyorK7PPXoaEhMjHx6funGcmP8qD08vMzLSuvPJKy8fHx4qIiLAeeeQR69ChQ5Zlnfjob2JiohUWFmZ5e3tbjRo1svr162dlZ2cbrvr8WL58uSXJ6dWvXz/Lsk58VHXcuHFWRESE5evra/31r3+1tm7d6rCPY8eOWUOGDLFCQkIsf39/q2fPnnV6/M52zLKzs62//vWvVkhIiOXj42NdddVV1tChQ638/HxD7+jcOtN4zZ07t9L148aNs++Dc8y1MbvYzjHLOv2YVXwEurLX8uXL7fuoC+eZzbIs65wlHQAAgDPgnhEAAGAUYQQAABhFGAEAAEYRRgAAgFGEEQAAYBRhBAAAGEUYAQAARhFGAACAUYQRAABgFGEEAAAYRRgBAABG/T8ers3h/IGUjQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y = [1]*(numberLevels-nf) # this is the height of the signal. It doesnt matter, just height = 1\n",
    "fig, ax = plt.subplots()\n",
    "ax.stem(wavelengths, y, markerfmt=' ',linefmt='red')\n",
    "plt.title(\"The Lyman series. Wavelength(nm)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "Exercise"
    ]
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   "source": [
    "* In the graph above which line corresponds to smallest \"electron jump\"? Which line to the largest \"electron jump\"?"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questions\n",
    "\n",
    "1. In a separate notebook answer all the questions asked in cells labeled \"Exercise\".\n",
    "2. Find the wavelength at which each the series (Lyman, Balmer, Paschen...) converge\n",
    "3. Plot all the series\n",
    "4. Find the frequency at which each the series (Lyman, Balmer, Paschen...) converge\n",
    "5. Plot the Lyman series in terms of frequencies. Identify which line corresponds to the largest \"electron jump\".\n",
    "6. **Only if you think that the previous exercises were too easy**, go ahead and plot in a single graph all the series so that you can reproduce the first image of this notebook. (*I don't expect anyone to do this, but if you're having the time of your life with Python I want to make sure that you see that there's always more \"fun\" to be had*)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "* https://en.wikipedia.org/wiki/Hydrogen_spectral_series\n",
    "* https://www.khanacademy.org/science/physics/quantum-physics/atoms-and-electrons/a/bohrs-model-of-hydrogen \n",
    "* https://link.springer.com/chapter/10.1007%2F978-3-319-14316-3_2"
   ]
  }
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