added books

1 files changed, 126 insertions, 105 deletions

diff --git a/Modern_Physics/Chapter7.ipynb b/Modern_Physics/Chapter7.ipynb
index 5f1ccec9..b8966938 100755
--- a/Modern_Physics/Chapter7.ipynb
+++ b/Modern_Physics/Chapter7.ipynb
@@ -1,7 +1,6 @@
 {
  "metadata": {
-  "name": "",
-  "signature": "sha256:75c249ea2e8c0a6e5f6f1e7aa12f02f35c3e7e62df28f6611e18b53d1b7e6dcd"
+  "name": "Chapter7"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -13,54 +12,34 @@
      "level": 1,
      "metadata": {},
      "source": [
-      "Chapter 7: Tunneling Phenomena"
+      "Chapter 7:The Hydrogen Atom in Wave Mechanics"
      ]
     },
     {
      "cell_type": "heading",
-     "level": 2,
+     "level": 1,
      "metadata": {},
      "source": [
-      "Example 7.1, page no. 235"
+      "Example 7.2 Page 213"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "\n",
-      "\n",
+      "#initiation of variable\n",
+      "from math import exp\n",
       "import math\n",
+      "from scipy import integrate\n",
+      "# calculating radial probability  P= (4/ao^3)*integral(r^2 * e^(-2r/ao)) between the limits 0 and ao for r\n",
       "\n",
-      "#Variable declaration\n",
-      "h = 1.973 * 10**3       #planck's constant (eV.A'/c)\n",
-      "me = 511 * 10**3        #mass of electron (eV/c^2)\n",
-      "U = 10.0\n",
-      "E = 7.0\n",
-      "L = 50.00               #thickness of layer (A')\n",
-      "\n",
-      "#Calculation\n",
-      "\n",
-      "a = math.sqrt(2*me*(U-E))/h\n",
-      "T=(1.0+(1.0/4.0)*(U**2/(E*(U-E)))*(math.sinh(a*L))**2)**-1\n",
-      "\n",
-      "#Result\n",
-      "\n",
-      "print \"The transmission coefficient for L=\",L,\"A' is\",round(T/10**-38,3),\"X 10^-38\"\n",
-      "\n",
-      "#(b)if the layer thickness is 1.00nm.\n",
-      "\n",
-      "#Variable Declaration\n",
-      "\n",
-      "L = 10          #thickness of layer (A')\n",
+      "#calculation\n",
+      "def integrand(x):\n",
+      "    return ((x**2)*exp(-x))/2.0\n",
+      "Pr=integrate.quad(integrand,0,2,args=());#simplifying where as x=2*r/a0; hence the limits change between 0 to 2\n",
       "\n",
-      "#Calculation\n",
-      "\n",
-      "T=(1.0+(1.0/4.0)*(U**2/(E*(U-E)))*(math.sinh(a*L))**2)**-1\n",
-      "\n",
-      "#Result\n",
-      "\n",
-      "print \"The transmission coefficient for L=\",L,\"A' is\",round(T/10**-7,3),\"X 10^-7\""
+      "#result\n",
+      "print \"Hence the probability of finding the electron nearer to nucleus is\",round(Pr[0],3);\n"
      ],
      "language": "python",
      "metadata": {},
@@ -69,41 +48,44 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "The transmission coefficient for L= 50.0 A' is 0.963 X 10^-38\n",
-        "The transmission coefficient for L= 10 A' is 0.657 X 10^-7\n"
+        "Hence the probability of finding the electron nearer to nucleus is 0.323\n"
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 2
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
-      "Example 7.2, page no. 236"
+      "Example 7.3 Page 213"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
+      "#initiation of variable\n",
+      "from math import exp\n",
+      "import math\n",
+      "from scipy import integrate\n",
+      "# employing the formula for probability distribution similarly as done in Exa-7.2 \n",
+      "#calculation\n",
+      "def integrand(x):\n",
+      "    return (1.0/8)*((4.0*x**2)-(4.0*x**3)+(x**4))*exp(-x)\n",
+      "Pr1= integrate.quad(integrand,0,1,args=())             #x=r/ao; similrly limits between 0 and 1.\n",
       "\n",
-      "#Variable declaration\n",
-      "\n",
-      "e = 1.6 * 10 ** -19     #charge of electron (C)\n",
-      "I = 1.00 * 10 ** -3     #electron current(A)\n",
-      "T = 0.657 *10**-7       #Transmission coefficient\n",
-      "\n",
-      "#Calculation\n",
-      "\n",
-      "Ne = I / e\n",
-      "Nadj = Ne * T\n",
-      "Iadj = Nadj * e\n",
+      "#result\n",
+      "print\"The probability for l=0 electron is\",round(Pr1[0],5)\n",
       "\n",
-      "#Result\n",
+      "#part2\n",
+      "def integrand(x):\n",
+      "    return (1.0/24)*(x**4)*(exp(-x))\n",
+      "Pr2=integrate.quad(integrand,0,1);                            #x=r/ao; similarly limits between 0 and 1.\n",
       "\n",
-      "print \"The number of electrons per second continuing on the adjacent wire is\",round(Nadj/10**8,2),\"X 10^8 and the transmitted current is\",round(Iadj/10**-12,1),\"pA.\""
+      "#result\n",
+      "print\"The probability for l=1 electron is\",round(Pr2[0],5)\n"
      ],
      "language": "python",
      "metadata": {},
@@ -112,46 +94,38 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "The number of electrons per second continuing on the adjacent wire is 4.11 X 10^8 and the transmitted current is 65.7 pA.\n"
+        "The probability for l=0 electron is 0.03432\n",
+        "The probability for l=1 electron is 0.00366\n"
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 4
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
-      "Example 7.5, page no. 241"
+      "Example 7.4 Page 215"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      "\n",
-      "\n",
+      "#initiation of variable\n",
+      "from math import exp, sqrt\n",
       "import math\n",
+      "from scipy import integrate\n",
+      "l=1.0;         #given value of l\n",
       "\n",
-      "#Variable Declaration\n",
-      "\n",
-      "e = 1.6 * 10 **-19      #charge of electron(C)\n",
-      "f = 1.0*10**30          #collision frequency (s^-1.cm^-2)\n",
-      "Ec = 5.5 * 10 ** 10     \n",
-      "V = 10 * 10 ** 3        #potential difference(V)\n",
-      "d = 0.010 * 10**-3      #plate separation(m)\n",
-      "\n",
-      "#Calculation\n",
-      "\n",
-      "E = V /d\n",
-      "Te = math.exp(-Ec/E)\n",
-      "rate = f * Te\n",
-      "I = e * rate\n",
+      "#calculation\n",
+      "am1=sqrt(l*(l+1));      #angular momentum==sqrt(l(l+1)) h\n",
+      "l=2.0                     #given l\n",
+      "am2=sqrt(l*(l+1));\n",
       "\n",
       "#result\n",
-      "\n",
-      "print \"The tunneling current is\",round(I/10**-12,2),\"pA.\""
+      "print\"The angular momenta are found out to be\", round(am1,3),\" h and\",round(am2,3),\" h respectively for l=1 and l=2.\";\n"
      ],
      "language": "python",
      "metadata": {},
@@ -160,55 +134,102 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "The tunneling current is 0.21 pA.\n"
+        "The angular momenta are found out to be 1.414  h and 2.449  h respectively for l=1 and l=2.\n"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 6
     },
     {
      "cell_type": "heading",
      "level": 2,
      "metadata": {},
      "source": [
-      "Example 7.6, page no. 244"
+      "Example 7.5 Page 216"
      ]
     },
     {
      "cell_type": "code",
      "collapsed": false,
      "input": [
-      " \n",
-      "\n",
-      "import math\n",
-      "\n",
-      "#Variable declaration\n",
-      "\n",
-      "Zth = 90            #atomic number of thorium\n",
-      "Zdth = 88           #atomic number of thorium's daughter nucleus\n",
-      "E = 4.05            #energy of ejected alphas(MeV)\n",
-      "Zpo = 84            #atomic number of polonium\n",
-      "Zdpo = 82           #atomic number of polonium's daughter nucleus\n",
-      "Epo = 8.95            #energy of ejected alphas(MeV)\n",
-      "R = 9.00            #nucleus size(fm)\n",
-      "r0 = 7.25           #Bohr radius of alpha(fm)\n",
-      "E0 = 0.0993         #(MeV)\n",
-      "f = 10 ** 21        #collision frequency(Hz)\n",
-      "\n",
-      "\n",
-      "#Calculation\n",
+      "#initiation of variable\n",
+      "from math import sqrt\n",
+      "print \"The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\";\n",
+      "print \"Length of the vector as found out previously is %.2f*h.\",round(sqrt(6),4);#angular momentum==sqrt(l(l+1)) h"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\n",
+        "Length of the vector as found out previously is %.2f*h. 2.4495\n"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.6 Page 223"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#initiation of variable\n",
+      "uz=9.27*10**-24; t=1.4*10**3; x=3.5*10**-2;    #various constants and given values\n",
+      "m=1.8*10**-25;v=750;                        # mass and velocity of the particle\n",
       "\n",
-      "Te = math.exp(-4*math.pi*Zdth*math.sqrt((E0/E))+ 8 * math.sqrt(Zdth*R/r0))\n",
-      "rate = f * Te\n",
-      "t = math.log(2)/rate\n",
-      "Tep = math.exp(-4*math.pi*Zdpo*math.sqrt((E0/Epo))+ 8 * math.sqrt(Zdpo*R/r0))\n",
-      "ratep = f * Tep\n",
-      "tp = math.log(2)/ratep\n",
+      "#calculation\n",
+      "d=(uz*t*(x**2))/(m*(v**2));                  #net separtion \n",
       "\n",
+      "#result\n",
+      "print\"The distance of separation in mm is\",round(d*10**3,3);"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The distance of separation in mm is 0.157\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.7 Page 227"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#initiation of variable\n",
+      "n1=1.0;n2=2.0;hc=1240.0;    #hc=1240 eV.nm\n",
+      "E=(-13.6)*((1/n2**2)-(1/n1**2));   #Energy calculation\n",
       "\n",
-      "#Result\n",
+      "#calculation\n",
+      "w=hc/E;                   #wavelength\n",
+      "u=9.27*10**-24; B=2;          #constants\n",
+      "delE= u*B/(1.6*10**-19);     #change in energy\n",
+      "delw=((w**2/hc))*delE;             #change in wavelength\n",
       "\n",
-      "print \"The half life of thorium is\",round(t/10**17,1),\"X 10^17 s and that of polonium is\",round(tp/10**-10,1),\"X 10^-10 s.\""
+      "#result\n",
+      "print\"The change in wavelength in nm. is\",round(delw,4);"
      ],
      "language": "python",
      "metadata": {},
@@ -217,11 +238,11 @@
        "output_type": "stream",
        "stream": "stdout",
        "text": [
-        "The half life of thorium is 5.4 X 10^17 s and that of polonium is 8.4 X 10^-10 s.\n"
+        "The change in wavelength in nm. is 0.0014\n"
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 12
     }
    ],
    "metadata": {}