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 {
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	   "metadata": {},
	   "source": [
       "# Chapter 6: Classical Statistics and Quantum Statistics"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.10: Number_of_microstates_formed_by_particles_obeying_Fermi_Dirac_statistics.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.10: Page-350 (2008)\n",
"clc; clear;\n",
"g1 = 8, g2 = 10;    // Total number of cells in the first and the second compartments respectively\n",
"n1 = 3, n2 = 4;    // Given number of cells in the first and the second compartments respectively for given macrostate\n",
"W_34 = factorial(g1)/(factorial(n1)*factorial(g1 - n1))*factorial(g2)/(factorial(n2)*factorial(g2 - n2));    // Total number of microstates in the macrostate (3, 4)\n",
"printf('\nThe total number of microstates in the macrostate (%d, %d) = %d', n1, n2, W_34);\n",
"\n",
"// Result\n",
"// The total number of microstates in the macrostate (3, 4) = 11760 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.11: Fermi_energy_and_internal_energy_for_metallic_silver_at_0_K.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.11: Page-351 (2008)\n",
"clc; clear;\n",
"h = 6.6e-034;    // Planck's constant, Js\n",
"m = 9.1e-031;    // Mass of an electron, kg\n",
"e = 1.6e-019;    // Energy equivalent of 1 eV, J\n",
"rho = 10.5;    // Density of silver, g/cc\n",
"A = 108;    // Atomic weight of Ag, g/mole\n",
"N_A = 6.023e+023;    // Avogadro's number\n",
"E_F0 = h^2/(8*m)*(3*N_A*rho*1e+006/(%pi*A))^(2/3);     // Fermi energy of silver at 0 K, J\n",
"U = 3/5*(N_A*rho*1e+006/A)*E_F0;    // Internal energy of the electron gas per unit volume at 0 K, J/metre-cube\n",
"printf('\nThe Fermi energy of silver at 0 K = %3.1f eV', E_F0/e);\n",
"printf('\nThe internal energy of the electron gas per unit volume at 0 K = %4.2e J/cubic-metre', U);\n",
"\n",
"// Result\n",
"// The Fermi energy of silver at 0 K = 5.5 eV\n",
"// The internal energy of the electron gas per unit volume at 0 K = 3.07e+010 J/cubic-metre "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.12: Number_of_conduction_electrons_per_cc_in_silver_at_0_K.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.12: Page-351 (2008)\n",
"clc; clear;\n",
"h = 6.6e-034;    // Planck's constant, Js\n",
"m = 9.1e-031;    // Mass of an electron, kg\n",
"e = 1.6e-019;    // Energy equivalent of 1 eV, J\n",
"E_F0 = 5.48;     // Fermi energy of silver at 0 K, eV\n",
"N_bar = (8*m/h^2)^(3/2)*%pi/3*(E_F0*e)^(3/2);    // Number density of conduction electrons in silver at 0 K, per cc\n",
"printf('\nThe number density of conduction electrons in silver at 0 K = %3.1e per cc', N_bar*1e-006);\n",
"\n",
"// Result\n",
"// The number density of conduction electrons in silver at 0 K = 5.9e+022 per cc "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.13: Fermi_energy_of_conduction_electrons_in_cesium.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.13: Page-351 (2008)\n",
"clc; clear;\n",
"h = 6.6e-034;    // Planck's constant, Js\n",
"m = 9.1e-031;    // Mass of an electron, kg\n",
"e = 1.6e-019;    // Energy equivalent of 1 eV, J\n",
"E_F0_Be = 14.44      // Fermi energy of Be at 0 K, eV\n",
"N_bar_Be = 24.2e+022;   // Number density of conduction electrons in Be at 0 K, per cc\n",
"N_bar_Cs = 0.91e+022;    // Number density of conduction electrons in Cs at 0 K, per cc\n",
"E_F0_Cs = E_F0_Be*(N_bar_Cs/N_bar_Be)^(2/3);    // Fermi energy of conduction electrons in cesium, eV\n",
"printf('\nThe Fermi energy of conduction electrons in cesium = %5.3f eV', E_F0_Cs);\n",
"\n",
"// Result\n",
"// The Fermi energy of conduction electrons in cesium = 1.621 eV \n",
"// The answer is given wrongly in the textbook"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.1: Probability_of_distribution_of_distinguishable_particles.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.1: Page-345 (2008)\n",
"clc; clear;\n",
"n = 14;    // Total number of particles\n",
"C = 2;    // Total number of compartments\n",
"N_micro = C^n;    // Total number of microstates\n",
"n1 = [10 7 14];    // Set of number of particles in first compartment\n",
"n2 = [4 7 0];    // Set of number of particles in second compartment\n",
"for i = 1:1:3\n",
"    W = factorial(n1(i) + n2(i))/(factorial(n1(i))*factorial(n2(i)));\n",
"    P = W/N_micro;\n",
"    printf('\nThe probability of microstate (%d, %d) = %8.6f', n1(i), n2(i), P);\n",
"end\n",
"\n",
"// Result\n",
"// The probability of microstate (10, 4) = 0.061096\n",
"// The probability of microstate (7, 7) = 0.209473\n",
"// The probability of microstate (14, 0) = 0.000061 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.6: Most_probable_distribution_for_total_energy.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.6: Page-348 (2008)\n",
"clc; clear;\n",
"MAX = 10;\n",
"// Look for all the possible set of values for n1, n2 and n3\n",
"printf('\nThe most probable distribution is for ');\n",
"for i = 0:1:5  \n",
"    for j = 0:1:5\n",
"        for k = 0:1:5\n",
"      // Check for the condition and avoid repetition of set of values\n",
"            if ((i + j + k) == 5) & ((j+2*k) == 3) then \n",
"                W = factorial(i + j + k)/(factorial(i)*factorial(j)*factorial(k));\n",
"                if W > MAX then\n",
"                   printf('\nn1 = %d, n2 = %d and n3 = %d', i, j, k);\n",
"                end\n",
"            end\n",
"        end\n",
"    end\n",
"end\n",
"\n",
"// Result\n",
"// The most probable distribution is for \n",
"// n1 = 3, n2 = 1 and n3 = 1 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.8: Probability_for_a_Maxwell_Boltzmann_system_to_be_in_given_states.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.8: Page-349 (2008)\n",
"clc; clear;\n",
"k = 1.38e-016;    // Boltzmann constant, erg/K\n",
"T = 100;    // Given temperature, K\n",
"E1 = 0;    // Energy of the first state, erg\n",
"E2 = 1.38e-014;    // Energy of the second state, erg\n",
"E3 = 2.76e-014;    // Energy of the third state, erg\n",
"g1 = 2, g2 = 5, g3 = 4;    // Different ways of occuring for E1, E2 and E3 states\n",
"P1 = g1*exp(-E1/(k*T));    // Probability of occurence of state E1\n",
"P2 = g2*exp(-E2/(k*T));    // Probability of occurence of state E2\n",
"P3 = g3*exp(-E3/(k*T));    // Probability of occurence of state E3\n",
"PE_3 = P3/(P1+P2+P3);    // Probability for the system to be in any one microstates of E3\n",
"P0 = P1/(P1+P2+P3);    // Probability for the system to be in ground state\n",
"printf('\nThe probability for the system to be in any one microstates of E3 = %6.4f', PE_3);\n",
"printf('\nThe probability for the system to be in ground state = %5.3f', P0);\n",
"\n",
"// Result\n",
"// The probability for the system to be in any one microstates of E3 = 0.1236\n",
"// The probability for the system to be in ground state = 0.457 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 6.9: Number_of_microstates_in_the_given_macostate_of_a_Fermi_Dirac_system.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex6.9: Page-350 (2008)\n",
"clc; clear;\n",
"g1 = 6, g2 = 8;    // Total number of cells in the first and the second compartments respectively\n",
"n1 = 2, n2 = 3;    // Given number of cells in the first and the second compartments respectively for given macrostate\n",
"W_23 = factorial(g1)/(factorial(n1)*factorial(g1 - n1))*factorial(g2)/(factorial(n2)*factorial(g2 - n2));    // Total number of microstates in the macrostate (2, 3)\n",
"printf('\nThe total number of microstates in the macrostate (%d, %d) = %d', n1, n2, W_23);\n",
"\n",
"// Result\n",
"// The total number of microstates in the macrostate (2, 3) = 840 "
   ]
   }
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