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Diffstat (limited to 'Engineering_Physics_Aruldhas/Chapter9_1.ipynb')
| -rw-r--r-- | Engineering_Physics_Aruldhas/Chapter9_1.ipynb | 219 |
1 files changed, 190 insertions, 29 deletions
diff --git a/Engineering_Physics_Aruldhas/Chapter9_1.ipynb b/Engineering_Physics_Aruldhas/Chapter9_1.ipynb index 50e4b6bd..af5adbcc 100644 --- a/Engineering_Physics_Aruldhas/Chapter9_1.ipynb +++ b/Engineering_Physics_Aruldhas/Chapter9_1.ipynb @@ -1,6 +1,7 @@ { "metadata": { - "name": "Chapter9" + "name": "", + "signature": "sha256:d58e11c98e937b7ff914fc9567035f99fc6ab344053f332f140829887d0ef6cc" }, "nbformat": 3, "nbformat_minor": 0, @@ -11,25 +12,46 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": "9: Quantum Mechanics" + "source": [ + "9: Quantum Mechanics" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.1, Page number 202" + "source": [ + "Example number 9.1, Page number 202" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the De-Broglie wavelength of electron\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nV = 100; #Accelerating potential for electron(volt)\n\n#Calculation\nlamda = math.sqrt(150/V)*10**-10; #de-Broglie wavelength of electron(m)\n\n#Result\nprint \"The De-Broglie wavelength of electron is\",lamda, \"m\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V = 100; #Accelerating potential for electron(volt)\n", + "\n", + "#Calculation\n", + "lamda = math.sqrt(150/V)*10**-10; #de-Broglie wavelength of electron(m)\n", + "\n", + "#Result\n", + "print \"The De-Broglie wavelength of electron is\",lamda, \"m\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The De-Broglie wavelength of electron is 1.22474487139e-10 m\n" + "text": [ + "The De-Broglie wavelength of electron is 1.22474487139e-10 m\n" + ] } ], "prompt_number": 1 @@ -38,19 +60,44 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.2, Page number 203" + "source": [ + "Example number 9.2, Page number 203" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the De-Broglie wavelength of electron\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\nh = 6.626*10**-34; #Planck's constant(Js)\nm = 9.11*10**-31; #Mass of the electron(kg)\nEk = 10; #Kinetic energy of electron(eV)\n\n#Calculation\np = math.sqrt(2*m*Ek*e); #Momentum of the electron(kg-m/s)\nlamda = h/p ; #de-Broglie wavelength of electron from De-Broglie relation(m)\nlamda = lamda*10**9; #de-Broglie wavelength of electron from De-Broglie relation(nm)\nlamda = math.ceil(lamda*10**2)/10**2; #rounding off the value of lamda to 2 decimals\n\n#Result\nprint \"The de-Broglie wavelength of electron is\",lamda, \"nm\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "m = 9.11*10**-31; #Mass of the electron(kg)\n", + "Ek = 10; #Kinetic energy of electron(eV)\n", + "\n", + "#Calculation\n", + "p = math.sqrt(2*m*Ek*e); #Momentum of the electron(kg-m/s)\n", + "lamda = h/p ; #de-Broglie wavelength of electron from De-Broglie relation(m)\n", + "lamda = lamda*10**9; #de-Broglie wavelength of electron from De-Broglie relation(nm)\n", + "lamda = math.ceil(lamda*10**2)/10**2; #rounding off the value of lamda to 2 decimals\n", + "\n", + "#Result\n", + "print \"The de-Broglie wavelength of electron is\",lamda, \"nm\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The de-Broglie wavelength of electron is 0.39 nm\n" + "text": [ + "The de-Broglie wavelength of electron is 0.39 nm\n" + ] } ], "prompt_number": 2 @@ -59,25 +106,52 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.3, Page number 203. theoritical proof" + "source": [ + "Example number 9.3, Page number 203. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.4, Page number 203" + "source": [ + "Example number 9.4, Page number 203" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the uncertainty in position of electron\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nh = 6.626*10**-34; #Planck's constant(Js)\nm = 9.11*10**-31; #Mass of the electron(kg)\nv = 1.1*10**6; #Speed of the electron(m/s)\npr = 0.1; #precision in percent\n\n#Calculation\np = m*v; #Momentum of the electron(kg-m/s)\ndp = pr/100*p; #Uncertainty in momentum(kg-m/s)\nh_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\ndx = h_bar/(2*dp); #Uncertainty in position(m)\n\n#Result\nprint \"The uncertainty in position of electron is\",dx, \"m\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "m = 9.11*10**-31; #Mass of the electron(kg)\n", + "v = 1.1*10**6; #Speed of the electron(m/s)\n", + "pr = 0.1; #precision in percent\n", + "\n", + "#Calculation\n", + "p = m*v; #Momentum of the electron(kg-m/s)\n", + "dp = pr/100*p; #Uncertainty in momentum(kg-m/s)\n", + "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", + "dx = h_bar/(2*dp); #Uncertainty in position(m)\n", + "\n", + "#Result\n", + "print \"The uncertainty in position of electron is\",dx, \"m\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The uncertainty in position of electron is 5.26175358211e-08 m\n" + "text": [ + "The uncertainty in position of electron is 5.26175358211e-08 m\n" + ] } ], "prompt_number": 3 @@ -86,19 +160,43 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.5, Page number 203" + "source": [ + "Example number 9.5, Page number 203" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the uncertainty in energy of the excited state\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\ne = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\nh = 6.626*10**-34; #Planck's constant(Js)\ndt = 10**-8; #Uncertainty in time(s)\n\n#Calculation\nh_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\ndE = h_bar/(2*dt*e); #Uncertainty in energy of the excited state(m)\n\n#Result\nprint \"The uncertainty in energy of the excited state is\",dE, \"eV\"\n\n#answer given in the book is wrong", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "dt = 10**-8; #Uncertainty in time(s)\n", + "\n", + "#Calculation\n", + "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", + "dE = h_bar/(2*dt*e); #Uncertainty in energy of the excited state(m)\n", + "\n", + "#Result\n", + "print \"The uncertainty in energy of the excited state is\",dE, \"eV\"\n", + "\n", + "#answer given in the book is wrong" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The uncertainty in energy of the excited state is 3.2955020404e-08 eV\n" + "text": [ + "The uncertainty in energy of the excited state is 3.2955020404e-08 eV\n" + ] } ], "prompt_number": 4 @@ -107,19 +205,44 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.6, Page number 204" + "source": [ + "Example number 9.6, Page number 204" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the width of spectral line\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nc = 3*10**8; #Speed of light(m/s)\ndt = 10**-8; #Average lifetime(s)\nlamda = 400; #Wavelength of spectral line(nm)\n\n#Calculation\nlamda = lamda*10**-9; #Wavelength of spectral line(m)\n#From Heisenberg uncertainty principle,\n#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give\n#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda\nd_lamda = (lamda**2)/(4*math.pi*c*dt); #Width of spectral line(m)\n\n#Result\nprint \"The width of spectral line is\",d_lamda, \"m\"", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light(m/s)\n", + "dt = 10**-8; #Average lifetime(s)\n", + "lamda = 400; #Wavelength of spectral line(nm)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of spectral line(m)\n", + "#From Heisenberg uncertainty principle,\n", + "#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give\n", + "#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda\n", + "d_lamda = (lamda**2)/(4*math.pi*c*dt); #Width of spectral line(m)\n", + "\n", + "#Result\n", + "print \"The width of spectral line is\",d_lamda, \"m\"" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The width of spectral line is 4.24413181578e-15 m\n" + "text": [ + "The width of spectral line is 4.24413181578e-15 m\n" + ] } ], "prompt_number": 5 @@ -128,61 +251,99 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.7, Page number 204. theoritical proof" + "source": [ + "Example number 9.7, Page number 204. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.8, Page number 204. theoritical proof" + "source": [ + "Example number 9.8, Page number 204. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.9, Page number 205. theoritical proof" + "source": [ + "Example number 9.9, Page number 205. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.10, Page number 205. theoritical proof" + "source": [ + "Example number 9.10, Page number 205. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.11, Page number 205. theoritical proof" + "source": [ + "Example number 9.11, Page number 205. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.12, Page number 206. theoritical proof" + "source": [ + "Example number 9.12, Page number 206. theoritical proof" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.13, Page number 206. theoritical proof " + "source": [ + "Example number 9.13, Page number 206. theoritical proof " + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 9.14, Page number 207" + "source": [ + "Example number 9.14, Page number 207" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the probability of finding the electron\n\n#importing modules\nimport math\nfrom __future__ import division\nfrom scipy.integrate import quad\n\n#Variable declaration\na = 2*10**-10; # Width of 1D box(m)\nx1=0; # Position of first extreme of the box(m)\nx2=1*10**-10; # Position of second extreme of the box(m)\n\n#Calculation\ndef intg(x):\n return ((2/a)*(math.sin(2*math.pi*x/a))**2)\nS=quad(intg,x1,x2)[0]\n\n#Result\nprint \"The probability of finding the electron between x = 0 and x = 10**-10 is\",S", + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "from scipy.integrate import quad\n", + "\n", + "#Variable declaration\n", + "a = 2*10**-10; # Width of 1D box(m)\n", + "x1=0; # Position of first extreme of the box(m)\n", + "x2=1*10**-10; # Position of second extreme of the box(m)\n", + "\n", + "#Calculation\n", + "def intg(x):\n", + " return ((2/a)*(math.sin(2*math.pi*x/a))**2)\n", + "S=quad(intg,x1,x2)[0]\n", + "\n", + "#Result\n", + "print \"The probability of finding the electron between x = 0 and x = 10**-10 is\",S" + ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": "The probability of finding the electron between x = 0 and x = 10**-10 is 0.5\n" + "text": [ + "The probability of finding the electron between x = 0 and x = 10**-10 is 0.5\n" + ] } ], "prompt_number": 7 @@ -190,7 +351,7 @@ { "cell_type": "code", "collapsed": false, - "input": "", + "input": [], "language": "python", "metadata": {}, "outputs": [] |