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author | Jovina Dsouza | 2014-07-25 00:00:07 +0530 |
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committer | Jovina Dsouza | 2014-07-25 00:00:07 +0530 |
commit | cc0f90b966a13e6edc60165bc4d4d36844af4f2b (patch) | |
tree | 896d9488c2766babf34c3c9d895b0f9f730b0e54 /Engineering_Physics/Chapter4_1.ipynb | |
parent | a4206084fd8c2bd696ea4ae4012aa83534979456 (diff) | |
download | Python-Textbook-Companions-cc0f90b966a13e6edc60165bc4d4d36844af4f2b.tar.gz Python-Textbook-Companions-cc0f90b966a13e6edc60165bc4d4d36844af4f2b.tar.bz2 Python-Textbook-Companions-cc0f90b966a13e6edc60165bc4d4d36844af4f2b.zip |
adding book
Diffstat (limited to 'Engineering_Physics/Chapter4_1.ipynb')
-rwxr-xr-x | Engineering_Physics/Chapter4_1.ipynb | 347 |
1 files changed, 37 insertions, 310 deletions
diff --git a/Engineering_Physics/Chapter4_1.ipynb b/Engineering_Physics/Chapter4_1.ipynb index c2e7944f..5651b165 100755 --- a/Engineering_Physics/Chapter4_1.ipynb +++ b/Engineering_Physics/Chapter4_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:bd975238ecc341317a545ed613e73ea0b105f0af115e6d7857237510924e96a0" + "name": "Chapter4" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,61 +11,25 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "4: Diffraction" - ] + "source": "4: Quantum Physics" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.1, Page number 91" - ] + "source": "Example number 4.1, Page number 117" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "D = 50; #Distance between source and the screen(cm)\n", - "lamda = 6563; #Wavelength of light of parallel rays(A)\n", - "d = 0.385; #Width of the slit(mm)\n", - "n1 = 1; #Order of diffraction for first minimum\n", - "n2 = 5; #Order of diffraction for fifth minimum\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of light of parallel rays(cm)\n", - "d = d*10**-1; #Width of the slit(cm)\n", - "#As sin(theta1) = n*lambda/d = x1/D, solving for x1\n", - "x1 = n1*lamda*D/d; #Distance from the centre of the principal maximum to the first minimum(cm)\n", - "x1 = x1*10; #Distance from the centre of the principal maximum to the first minimum(mm)\n", - "x1 = math.ceil(x1*10**3)/10**3; #rounding off the value of x1 to 3 decimals\n", - "x2 = n2*lamda*D/d; #Distance from the centre of the principal maximum to the fifth minimum(cm)\n", - "x2 = x2*10; #Distance from the centre of the principal maximum to the fifth minimum(mm)\n", - "x2 = math.ceil(x2*10**3)/10**3; #rounding off the value of x2 to 3 decimals\n", - "\n", - "#Result\n", - "print \"The Distance from the centre of the principal maximum to the first minimum is\",x1, \"mm\"\n", - "print \"The Distance from the centre of the principal maximum to the fifth minimum is\",x2, \"mm\"\n", - "\n", - "#answer for x2 given in the book is wrong" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.62*10**-34; #planck's constant\nlamda = 1.2; #wavelength of photon(Angstrom)\ne = 1.6*10**-19; #conversion factor from J to eV\n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = (h*c)/(lamda*e); #energy of photon(eV)\nE=math.ceil(E*10)/10; #rounding off to 1 decimal\np = h/lamda; #momentum of photon(kg m/s)\n\n#Result\nprint \"energy of the photon is\",E,\"eV\"\nprint \"momentum of the photon is\",p,\"kg m/s\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The Distance from the centre of the principal maximum to the first minimum is 0.853 mm\n", - "The Distance from the centre of the principal maximum to the fifth minimum is 4.262 mm\n" - ] + "text": "energy of the photon is 10343.8 eV\nmomentum of the photon is 5.51666666667e-24 kg m/s\n" } ], "prompt_number": 1 @@ -75,405 +38,169 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.2, Page number 91" - ] + "source": "Example number 4.2, Page number 117" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "from __future__ import division\n", - "import math\n", - "\n", - "#Variable declaration\n", - "D = 0.04; #Diameter of circular aperture(cm)\n", - "f = 20; #Focal length of convex lens(cm)\n", - "lamda = 6000; #Wavelength of light used(A)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-8; #Wavelength of light used(cm)\n", - "#We have sin(theta) = 1.22*lambda/D = theta, for small theta\n", - "#For first dark ring\n", - "theta = 1.22*lamda/D; #The half angular width at central maximum(rad)\n", - "r1 = theta*f; #The half width of central maximum for first dark ring(cm)\n", - "r1 = r1*10**2;\n", - "#We have sin(theta) = 5.136*lambda/(%pi*D) = theta, for small theta\n", - "#For second dark ring\n", - "theta = 5.136*lamda/(math.pi*D); #The half angular width at central maximum(rad)\n", - "r2 = theta*f; #The half width of central maximum for second dark ring(cm)\n", - "r2 = r2*10**2;\n", - "r2 = math.ceil(r2*100)/100; #rounding off the value of r2 to 2 decimals\n", - "\n", - "#Result\n", - "print \"The radius of first dark ring is\",r1,\"*10**-2 cm\"\n", - "print \"The radius of second dark ring is\",r2,\"*10**-2 cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nnew = 900; #frequency(kHz)\nE1 = 10; #power radiated(kW)\n\n#Calculation\nE1 = E1*10**3; #power radiated(W)\nnew = new*10**3; #frequency(Hz)\nE = h*new; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The radius of first dark ring is 3.66 *10**-2 cm\n", - "The radius of second dark ring is 4.91 *10**-2 cm\n" - ] + "text": "number of photons emitted per second is 1.67714884696e+31\n" } ], - "prompt_number": 6 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.3, Page number 92" - ] + "source": "Example number 4.3, Page number 118" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "n = 2; #Order of diffraction\n", - "lamda = 650; #Wavelength of light used(nm)\n", - "d = 1.2*10**-3; #Distance between two consecutive slits of grating(cm)\n", - "\n", - "#Calculation\n", - "#We have sin(theta) = n*N*lambda = n*lambda/d, solving for theta\n", - "lamda = lamda*10**-9; #Wavelength of light used(m)\n", - "d = d*10**-2; #Distance between two consecutive slits of grating(m)\n", - "a=n*lamda/d;\n", - "theta = math.asin(a); #Angle at which the 650 nm light produces a second order maximum(rad)\n", - "theta = theta*57.2957795; #angle in degrees\n", - "theta = math.ceil(theta*10**2)/10**2; #rounding off the value of theta to 2 decimals\n", - "\n", - "#Result\n", - "print \"The angle at which the light produces a second order maximum is\",theta, \"degrees\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.63*10**-34; #planck's constant\nlamda = 5893; #wavelength of photon(Angstrom)\nE1 = 100; #power of lamp(W) \n\n#Calculation\nlamda = lamda*10**-10; #wavelength of photon(m)\nE = h*c/lamda; #energy of photon(J)\nN = E1/E; #number of photons emitted \n\n#Result\nprint \"number of photons emitted per second is\",N\nprint \"answer given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The angle at which the light produces a second order maximum is 6.22 degrees\n" - ] + "text": "number of photons emitted per second is 2.96279537456e+20\nanswer given in the book is wrong\n" } ], - "prompt_number": 7 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.4, Page number 92" - ] + "source": "Example number 4.4, Page number 118" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 650; #Wavelength of light used(nm)\n", - "N = 6000; #Number of lines per cm on grating\n", - "theta = 90; #Angle at which the highest spectral order is obtained(degrees)\n", - "\n", - "#Calculation\n", - "theta = theta*0.0174532925; #Angle at which the highest spectral order is obtained(rad)\n", - "#We have sin(theta) = n*N*lambda, solving for n\n", - "lamda = lamda*10**-9; #Wavelength of light used(m)\n", - "N = N*10**2; #Number of lines per m on grating\n", - "n = math.sin(theta)/(N*lamda); #The highest order of spectra with diffraction grating\n", - "n = math.ceil(n*10**3)/10**3; #rounding off the value of theta to 3 decimals\n", - "i,d = divmod(n, 1); #divides the value of n into integer and decimal parts where i is integer\n", - "\n", - "#Result\n", - "print \"value of n is\",n\n", - "print \"The highest order of spectra obtained with diffraction grating is\",i\n" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nc = 3*10**8; #velocity of light(m/sec)\nh = 6.6*10**-34; #planck's constant\nm0 = 9.1*10**-31; #mass of photon(kg)\ntheta = 30; #viewing angle(degrees)\nlamda = 2.8*10**-10; #wavelength of photon(m)\n\n#Calculation\nx = math.pi/180; #conversion factor from degrees to radians\ntheta = theta*x; #viewing angle(radian) \nlamda_dash = (2*h*(math.sin(theta/2))**2/(m0*c))+lamda; #wavelength of scattered radiation(m)\nlamda_dash = lamda_dash*10**10; #wavelength of scattered radiation(Angstrom)\nlamda_dash=math.ceil(lamda_dash*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint \"wavelength of scattered radiation is\",lamda_dash,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "value of n is 2.565\n", - "The highest order of spectra obtained with diffraction grating is 2.0\n" - ] + "text": "wavelength of scattered radiation is 2.80324 Angstrom\n" } ], - "prompt_number": 8 + "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.5, Page number 92" - ] + "source": "Example number 4.5, Page number 119" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "N = 4000; #Number of lines per cm on grating\n", - "#For Blue Line\n", - "lamda1 = 450; #Wavelength of blue light(nm)\n", - "n1 = 3; #Order of diffraction spectrum\n", - "#For Red Line\n", - "lamda2 = 700; #Wavelength of red light(nm)\n", - "n2 = 2; #Order of diffraction spectrum\n", - "\n", - "#Calculation\n", - "N = N*10**2; #Number of lines per m on grating\n", - "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", - "lamda2 = lamda2*10**-9; #Wavelength of red light(m)\n", - "#We have sin(theta) = n*N*lambda, solving for sin(theta)\n", - "sin_theta_3 = n1*N*lamda1; #Sine of angle at third order diffraction \n", - "sin_theta_2 = n2*N*lamda2; #Sine of angle at second order diffraction\n", - "\n", - "#Result\n", - "print \"Sine of angle at third order diffraction is\",sin_theta_3\n", - "print \"Sine of angle at second order diffraction is\",sin_theta_2 \n", - "#Check for overlapping\n", - "if (sin_theta_2-sin_theta_3)<0.05:\n", - " print \"The two orders overlap\"\n", - "else:\n", - " print \"The two orders do not overlap\" " - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.6*10**-34; #planck's constant\nm = 0.040; #mass of bullet(kg)\nv = 1; #speed of bullet(km/s)\n\n#Calculation\nv = v*10**3; #speed of bullet(m/s)\np = m*v; #momemtun of bullet(kg m/s)\nlamda = h/p; #deBroglie wavelength(m)\nlamda = lamda*10**10; #deBroglie wavelength(Angstrom)\n\n#Result\nprint \"deBroglie wavelength is\",lamda,\"Angstrom\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "Sine of angle at third order diffraction is 0.54\n", - "Sine of angle at second order diffraction is 0.56\n", - "The two orders overlap\n" - ] + "text": "deBroglie wavelength is 1.65e-25 Angstrom\n" } ], - "prompt_number": 9 + "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.6, Page number 93" - ] + "source": "Example number 4.6, Page number 119" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "n = 1; #Order of diffraction spectrum\n", - "N = 6000; #Number of lines per cm on diffraction grating\n", - "D = 2; #Distance of screen from the source(m)\n", - "lamda1 = 400; #Wavelength of blue light(nm)\n", - "lamda2 = 750; #Wavelength of blue light(nm)\n", - "\n", - "#Calculation\n", - "N = N*10**2; #Number of lines per m on grating\n", - "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", - "lamda2 = lamda2*10**-9; #Wavelength of blue light(m)\n", - "#We have sin(theta1) = n*N*lamda1, solving for theta1\n", - "theta1 = math.asin(n*N*lamda1); #Angle at first order diffraction for Blue light(rad)\n", - "theta1_d = theta1*57.2957795; #Angle at first order diffraction for Blue light(degrees)\n", - "theta2 = math.asin(n*N*lamda2); #Angle at first order diffraction for Red light(rad)\n", - "theta2_d = theta2*57.2957795; #Angle at first order diffraction for Red light(degrees)\n", - "x1 = D*math.tan(theta1); #Half width position at central maximum for blue color(m)\n", - "x2 = D*math.tan(theta2); #Half width position at central maximum for red color(m)\n", - "x = x2-x1; #width of first order spectrum on the screen(m)\n", - "x = x*10**2; #width of first order spectrum on the screen(cm)\n", - "x = math.ceil(x*10**2)/10**2; #rounding off the value of x to 2 decimals\n", - "\n", - "#Result\n", - "print \"The width of first order spectrum on the screen is\",x, \"cm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of particle(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy of particle is\",E,\"J or\",E_eV,\"eV\" ", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The width of first order spectrum on the screen is 51.34 cm\n" - ] + "text": "energy of particle is 6.02231407794e-18 J or 37.6 eV\n" } ], - "prompt_number": 10 + "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.7, Page number 93" - ] + "source": "Example number 4.7, Page number 120" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "w = 5; #Width of the grating(cm)\n", - "N = 32; #Number of lines per mm on grating\n", - "lamda = 640; #Wavelength of light(nm)\n", - "n = 2; #Order of diffraction\n", - "\n", - "#Calculation\n", - "N= N*10; #Number of lines per cm on grating\n", - "N0 = w*N; #Total number of lines on the grating\n", - "d_lambda = lamda/(n*N0); #Separation between wavelengths(nm)\n", - "\n", - "#Result\n", - "print \"The separation between wavelengths which the grating can just resolve is\",d_lambda, \"nm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn = 1; #lowest energy state\na = 4; #width of well(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.6025*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE = (n**2)*(h**2)/(8*m*(a**2)); #energy of particle(J)\nE_eV = E/e; #energy of particle(eV)\nE_eV=math.ceil(E_eV*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint \"minimum energy of electron is\",E,\"J or\",E_eV,\"eV\" ", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The separation between wavelengths which the grating can just resolve is 0.2 nm\n" - ] + "text": "minimum energy of electron is 3.76394629871e-21 J or 0.0235 eV\n" } ], - "prompt_number": 11 + "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.8, Page number 93" - ] + "source": "Example number 4.8, Page number 120" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "\n", - "#Variable declaration\n", - "lamda = 550; #Wavelength of light(nm)\n", - "D = 3.2; #Diameter of circular lens(cm)\n", - "f = 24; #Focal length of the lens(cm) \n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of light(m)\n", - "D = D*10**-2; #Diameter of circular lens(m)\n", - "theta_min = 1.22*lamda/D; #Minimum angle of resolution provided by the lens(rad)\n", - "#As delta_x/f = theta_min, solving for delta_x\n", - "f = f*10**-2; #Focal length of the lens(m) \n", - "delta_x = theta_min*f; #Separation of the centres of the images in the focal plane of lens(m)\n", - "delta_x = delta_x*10**6; #Separation of the centres of the images in the focal plane of lens(micro m)\n", - " \n", - "#Result\n", - "print \"The separation of the centres of the images in the focal plane is\",round(delta_x), \"micro-metre\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1; #lowest energy state\nn2 = 6; #for 6th excited state\na = 0.1; #width of box(nm)\nh = 6.625*10**-34; #planck's constant\ne = 1.602*10**-19; #conversion factor from J to eV\nm = 9.11*10**-31; #mass of electron(kg)\n\n#Calculation\na = a*10**-9; #width of box(m)\nE1 = (n1**2)*(h**2)/(8*m*(a**2)); #energy of electron in ground state(J)\nE6 = (n2**2)*(h**2)/(8*m*(a**2)); #energy of electron in excited state(J)\nE = E6-E1; #energy required to excite the electron(J)\nE_eV = E/e; #energy required to excite the electron(eV)\nE_eV=math.ceil(E_eV*10)/10; #rounding off to 1 decimal\n\n#Result\nprint \"energy required to excite the electron is\",E,\"J or\",E_eV,\"eV\" \nprint \"answer for energy in eV given in the book is wrong\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The separation of the centres of the images in the focal plane is 5.0 micro-metre\n" - ] + "text": "energy required to excite the electron is 2.10780992728e-16 J or 1315.8 eV\nanswer for energy in eV given in the book is wrong\n" } ], - "prompt_number": 12 + "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 4.9, Page number 94" - ] + "source": "Example number 4.9, Page number 121" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \n", - "#importing modules\n", - "import math\n", - "from __future__ import division\n", - "\n", - "#Variable declaration\n", - "lamda = 550; #Wavelength of light(nm)\n", - "D = 20; #Diameter of objective of telescope(cm)\n", - "d = 6; #Distance of two points from the objective of telescope(km)\n", - "\n", - "#Calculation\n", - "lamda = lamda*10**-9; #Wavelength of light(m)\n", - "D = D*10**-2; #Diameter of objective of telescope(m)\n", - "d = d*10**3; #Distance of two points from the objective of telescope(m)\n", - "theta = 1.22*lamda/D; #Angular separation between two points(rad)\n", - "x = theta*d; #Linear separation between two points(m)\n", - "x = x*10**3; #Linear separation between two points(mm)\n", - "\n", - "#Result\n", - "print \"The linear separation between two points is\",x, \"mm\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nh = 6.625*10**-34; #planck's constant\nc = 3*10**8; #velocity of light(m/sec)\nm0 = 9.11*10**-31; #rest mass of electron(kg)\nphi = 90; #angle of scattering(degrees)\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi = phi*x; ##angle of scattering(radian)\ndelta_lamda = h*(1-math.cos(phi))/(m0*c); #change in wavelength(m)\n\n#Result\nprint \"change in wavelength of X-ray photon is\",delta_lamda,\"m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The linear separation between two points is 20.13 mm\n" - ] + "text": "change in wavelength of X-ray photon is 2.42407610684e-12 m\n" } ], - "prompt_number": 13 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] + "prompt_number": 9 } ], "metadata": {} |