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authorJovina Dsouza2014-07-25 00:00:07 +0530
committerJovina Dsouza2014-07-25 00:00:07 +0530
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tree896d9488c2766babf34c3c9d895b0f9f730b0e54 /Engineering_Physics/Chapter4_1.ipynb
parenta4206084fd8c2bd696ea4ae4012aa83534979456 (diff)
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adding book
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-rwxr-xr-xEngineering_Physics/Chapter4_1.ipynb347
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": {}