{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 10: Statistical Physics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10.1: Various_Speeds_obtained_from_maxwell_speed_distribution.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear\n", "clc\n", "disp('Exa-10.1'); //Theoretical Question\n", "//**Install and use maxim tool for symbolic integration. remove the '//'(comment markings) below and run the program.\n", "//Vm=integrate('(v^3)*(e^(-b*v^2))','x',0,%infi);\n", "//rest of the results follow from above\n", "printf('The average speed is found out to be (8*k*T/m)^1/2)\n'); \n", "printf('The RMS speed is (3*k*T/m)^1/2\n');\n", "printf('The Most probable speed is found out to be (2*k*T/m)^1/2 \n where all the symbols used are conventional constants.');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10.2: Frequency_distribution_of_emitted_light.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear\n", "clc\n", "disp('Exa-10.2'); //The solution is purely theoretical and involves a lot of approximations.\n", "printf('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');\n", "T=6000; //temperature for sun\n", "delf=7.14*10^-7*sqrt(T);.....//change in frequency\n", "printf('The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is %.1e times the frequency of the light.',delf);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10.3: Solution_for_a_and_b.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear\n", "clc\n", "disp('Exa-10.3(a)');\n", "kT=0.0252;E=10.2 // at room temperature, kT=0.0252 standard value and given value of E\n", "n2=2;n1=1; g2=2*(n2^2);g1=2*(n1^2); //values for ground and excited states\n", "t=(g2/g1)*%e^(-E/kT); //fraction of atoms\n", "printf('The number of hydrogen atoms required is %e which weighs %e Kg\n',1/t,(1/t)*(1.67*10^-27));\n", "disp('Ex-10.3(b)');\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", "printf('The value of temperature at which 1/10 atoms are in excited state is %.3f K',T);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10.4: Solution_for_a_and_b.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear\n", "clc\n", "disp('Exa-10.4(a)'); //theoretical\n", "printf('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", "disp('Ex-10.4(b)');\n", "uB=5.79*10^-4; //for a typical atom\n", "t=1.1;k=8.65*10^-5; //ratio and constant k\n", "T=2*uB/(log(t)*k); //temperature\n", "printf('The value of temperature ar which the given ratio exists is %.2f K',T);" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 10.5: Fermi_Energy_Ef_for_sodium.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "clear\n", "clc\n", "disp('Exa-10.5');\n", "p=0.971; A=6.023*10^23; m=23.0; // various given values and constants\n", "c= (p*A/m)*10^6; // atoms per unit volume\n", "hc=1240; mc2=0.511*10^6; // hc=1240 eV.nm\n", "E= ((hc^2)/(2*mc2))*(((3/(8*%pi))*c)^(2/3)); //value of fermi energy\n", "printf('The fermi energy for sodium is %f eV',E*10^-18);//multiply by 10^-18 to convert metres^2 term to nm^2" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }