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diff --git a/Modern_Physics/Chapter10.ipynb b/Modern_Physics/Chapter10.ipynb index a9cbc233..6135c0d0 100755 --- a/Modern_Physics/Chapter10.ipynb +++ b/Modern_Physics/Chapter10.ipynb @@ -1,7 +1,7 @@ { "metadata": { - "name": "", - "signature": "sha256:1d13a558dd2cc62e2c7ada350fc7a07d9283efcbc790578d0711fd6c96f50df0" + "name": "Chapter10", + "signature": "sha256:e4e2027717708d18dd95ce338ad24e83f0d7666653044656429dafb0b39af784" }, "nbformat": 3, "nbformat_minor": 0, @@ -13,7 +13,7 @@ "level": 1, "metadata": {}, "source": [ - "Chapter 10: Statistical Physics" + "Chapter 10:Statistical Physics" ] }, { @@ -21,64 +21,22 @@ "level": 2, "metadata": {}, "source": [ - "Example 10.1, page no. 340" + "Example 10.2 Page 307" ] }, { "cell_type": "code", "collapsed": false, "input": [ - "\n", - "\n", - "import math\n", - "\n", - "#Variable declaration\n", - "\n", - "n1 = 1 #Ground state\n", - "n2 = 2 #First excited state\n", - "n3 = 3 #second excited state\n", - "T = 300 #room temperature(K)\n", - "kb = 8.617 * 10 **-5 #Boltzmann constant(eV/K)\n", - "\n", - "#Calculation\n", - "\n", - "E1 = -13.6 / n1 ** 2\n", - "g1 = 2 * n1 ** 2\n", - "E2 = -13.6 / n2 ** 2\n", - "g2 = 2 * n2 ** 2\n", - "E3 = -13.6 / n3 ** 2\n", - "g3 = 2 * n3 ** 2\n", - "N3 = g3 * math.exp(-E3/(kb*T))\n", - "N2 = g2 * math.exp(-E2/(kb*T))\n", - "N1 = g1 * math.exp(-E1/(kb*T))\n", - "ratio1 = N2 / N1\n", - "ratio2 = N3 / N1\n", - "\n", - "#results\n", - "\n", - "print \"(a) We can see that n2/n1=\",round(ratio1),\"and n3/n1=\",round(ratio2),\"essentially all atoms are in ground state.\"\n", - "\n", - "\n", - "#Variable Declaration\n", - "\n", - "T = 20000 #Temperature(K)\n", - "\n", - "#Calculation\n", - "\n", - "N3 = g3 * math.exp(-E3/(kb*T))\n", - "N2 = g2 * math.exp(-E2/(kb*T))\n", - "N1 = g1 * math.exp(-E1/(kb*T))\n", - "ratio1 = N2 / N1\n", - "ratio2 = N3 / N1\n", + "#initiation of variable\n", + "from math import sqrt\n", + "#The solution is purely theoretical and involves a lot of approximations.\n", + "print\"The value of shift in frequency was found out to be delf=7.14*fo*10^-7*sqrt(T) for a star composing of hydrogen atoms at a temperature T.\";\n", + "T=6000.0; #temperature for sun\n", + "delf=7.14*10**-7*sqrt(T);#change in frequency\n", "\n", "#result\n", - "\n", - "print \"(b) n2/n1=\",round(ratio1,5),\"and n3/n1=\",round(ratio2,5)\n", - "\n", - "\n", - "ratio3 = N3 / N2\n", - "\n", - "print \"(c) S(3->2)/S(2->1)=\",round(ratio3,2)" + "print\"The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is\",delf,\" times the frequency of the light.\"" ], "language": "python", "metadata": {}, @@ -87,63 +45,42 @@ "output_type": "stream", "stream": "stdout", "text": [ - "(a) We can see that n2/n1= 0.0 and n3/n1= 0.0 essentially all atoms are in ground state.\n", - "(b) n2/n1= 0.01076 and n3/n1= 0.00809\n", - "(c) S(3->2)/S(2->1)= 0.75\n" + "The value of shift in frequency was found out to be delf=7.14*fo*10^-7*sqrt(T) for a star composing of hydrogen atoms at a temperature T.\n", + "The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is 5.53062021838e-05 times the frequency of the light.\n" ] } ], - "prompt_number": 3 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ - "Example 10.2, page no. 345" + "Example 10.3 Page 309" ] }, { "cell_type": "code", "collapsed": false, "input": [ + "#initiation of variable\n", + "from math import sqrt,pi, exp, log\n", + "kT=0.0252;E=10.2 # at room temperature, kT=0.0252 standard value and given value of E\n", "\n", - "\n", - "import math\n", - "\n", - "#Variable Declaration\n", - "\n", - "m = 3.34 * 10 ** -27 #mass of hydrogen(kg)\n", - "kbT = 3.77 * 10 ** -21 #kb * T (eV)\n", - "N = 6.02 * 10 ** 23 #avogadro's number\n", - "V = 22.4 * 10 ** -3 #Volume of H2 gas (m^3)\n", - "h = 1.055 * 10 ** -34 #Planck's constant (J.s)\n", - "\n", - "#Calculation\n", - "\n", - "r = (N/V)* h ** 3 / (8 * (m * kbT)**1.5)\n", + "#calculation\n", + "n2=2;n1=1; g2=2*(n2**2);g1=2*(n1**2); #values for ground and excited states\n", + "t=(g2/g1)*exp(-E/kT); #fraction of atoms\n", "\n", "#result\n", + "print\"The number of hydrogen atoms required is %.1e\" %(1.0/t),\" which weighs %.0e\" %((1/t)*(1.67*10**-27)),\"Kg\"\n", "\n", - "print \"(a) (N/V)h^3/(8*(mkbT)^3/2)=\",round(r/10**-8,2),\"X10^-8 is much less than 1, we conclude that even hydrogen is described by Maxwell-Boltzmann statistics.\"\n", - "\n", - "\n", - "\n", - "#Variable declaration\n", - "\n", - "d = 10.5 #density of silver (g/cm^3)\n", - "mw = 107.9 #Molar weight of silver (g/mol)\n", - "me = 9.109*10**-31 #mass of electron(kg)\n", - "kbT = 4.14 * 10 ** -21 #kb*T (J)\n", - "\n", - "#Calculation\n", - "\n", - "Ns = (d/mw)* N * 10 ** 6\n", - "r = (Ns)* h ** 3 / (8 * (me * kbT)**1.5)\n", + "#partb\n", + "t=0.1/0.9;k=8.65*10**-5 #fracion of atoms in case-2 is given\n", + "T=-E/(log(t/(g2/g1))*k); #temperature\n", "\n", "#result\n", - "\n", - "print \"(b) (N/V)h^3/(8*(mkbT)^3/2)=\",round(r/8,2),\"is greater than 1, we conclude that the Maxwell-Boltzmann statistics does not hold for electrons of silver.\"" + "print\"The value of temperature at which 1/10 atoms are in excited state in K is %.1e\" %round(T,3);" ], "language": "python", "metadata": {}, @@ -152,46 +89,77 @@ "output_type": "stream", "stream": "stdout", "text": [ - "(a) (N/V)h^3/(8*(mkbT)^3/2)= 8.83 X10^-8 is much less than 1, we conclude that even hydrogen is described by Maxwell-Boltzmann statistics.\n", - "(b) (N/V)h^3/(8*(mkbT)^3/2)= 4.64 is greater than 1, we conclude that the Maxwell-Boltzmann statistics does not hold for electrons of silver.\n" + "The number of hydrogen atoms required is 1.5e+175 which weighs 3e+148 Kg\n", + "The value of temperature at which 1/10 atoms are in excited state in K is 3.3e+04\n" ] } ], - "prompt_number": 5 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ - "Example 10.3, page no. 352" + "Example 10.4 Page 311" ] }, { "cell_type": "code", "collapsed": false, "input": [ - " \n", - "\n", - "import math\n", + "#initiation of variable\n", + "from math import log\n", + "#theoretical part a\n", + "print'The energy of interaction with magnetic field is given by uB and the degeneracy of the states are +-1/2 which are identical.\\nThe ratio is therefore pE2/pE1 which gives e^(-2*u*B/k*T)';\n", + "#partb\n", + "uB=5.79*10**-4; #for a typical atom\n", + "t=1.1;k=8.65*10**-5; #ratio and constant k\n", "\n", - "#Variable Declaration\n", + "#calculation\n", + "T=2*uB/(log(t)*k); #temperature\n", "\n", - "kB = 8.62 * 10 ** -5 #Boltzmann constant(eV/K)\n", - "T1 = 3000 #Cavity walls temperature(K)\n", - "T2 = 3.00 #Cavity walls temperature(K)\n", - "hc = 1.24 * 10 ** -4 #product of planck's constant and speed of light (eV.cm)\n", - "integration = 2.40 #value of integral(z^2/e^z-1,0,+inf)\n", - "\n", - "#Calculation\n", + "#result\n", + "print\"The value of temperature ar which the given ratio exists in K is\",round(T,3);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy of interaction with magnetic field is given by uB and the degeneracy of the states are +-1/2 which are identical.\n", + "The ratio is therefore pE2/pE1 which gives e^(-2*u*B/k*T)\n", + "The value of temperature ar which the given ratio exists in K is 140.46\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 10.5 Page 313" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#initiation of variable\n", + "from math import pi\n", + "p=0.971; A=6.023*10**23; m=23.0; # various given values and constants\n", "\n", - "NbyV_at_3000 = 8* math.pi * (kB * T1/hc)**3 * integration\n", - "NbyV_at_3 = 8* math.pi * (kB * T2/hc)**3 * integration\n", + "#calculation\n", + "c= (p*A/m)*10**6; # atoms per unit volume\n", + "hc=1240.0; mc2=0.511*10**6; # hc=1240 eV.nm\n", + "E= ((hc**2)/(2*mc2))*(((3/(8*pi))*c)**(2.0/3)); #value of fermi energy\n", "\n", "#result\n", - "\n", - "print \"N/V at 3000K is\",round(NbyV_at_3000/10**11,2),\"X 10^11 photons/cm^3. Likewise N/V at 3.00 K is\",round(NbyV_at_3/10**2,2),\"X 10^2 photons/cm^3\"\n", - "print \"Therefore the photon density decreases by a factor of\",round(NbyV_at_3000/NbyV_at_3/10**9),\" X 10^9 when the temperature drops from 3000K to 3.00K\"" + "print\"The fermi energy for sodium is\",round(E*10**-18,4),\"eV\";#multiply by 10^-18 to convert metres^2 term to nm^2" ], "language": "python", "metadata": {}, @@ -200,12 +168,11 @@ "output_type": "stream", "stream": "stdout", "text": [ - "N/V at 3000K is 5.47 X 10^11 photons/cm^3. Likewise N/V at 3.00 K is 5.47 X 10^2 photons/cm^3\n", - "Therefore the photon density decreases by a factor of 1.0 X 10^9 when the temperature drops from 3000K to 3.00K\n" + "The fermi energy for sodium is 3.1539 eV\n" ] } ], - "prompt_number": 7 + "prompt_number": 12 } ], "metadata": {} |