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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 13: Additional solved short answers"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_10: calculate_interplanar_spacing.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 10 , pg 349\n",
+"a=4.938 //lattice constant(in Angstrom)\n",
+"h=2\n",
+"k=2\n",
+"l=0 //since (h k l)=(2 2 0) miller indices\n",
+"d=a/sqrt(h^2+k^2+l^2) //spacing\n",
+"printf('spacing of (2 2 0) planes=')\n",
+"printf('d=%.3f Angstrom',d)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_12: find_the_wavelength.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 12_b_3 , pg 349\n",
+"Eg=0.8*1.6*10^-19 //bandgap (in J) (converting eV into J)\n",
+"h=6.625*10^-34 //plancks constant (in J s)\n",
+"c=3*10^8 //speed of light (in m/s)\n",
+"lam=(h*c)/Eg //wavelength\n",
+"printf('wavelength of light emitted (in m)is=')\n",
+"disp(lam)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_14: calculate_energy_of_scattered_photon.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 14_a_3 , pg 350\n",
+"lam=1.24*10^-13 //wavelength (in m)\n",
+"h=6.625*10^-34//plancksconstant(in J s)\n",
+"c=3*10^8//velocity of x-ray photon(in m/sec)\n",
+"m0=9.11*10^-31//rest mass of electron(in Kg)\n",
+"phi=(90*%pi)/180//angle of scattering (in radian) (converting degree into radian)\n",
+"delta_H=(h*(1-cos(phi)))/(m0*c)//change in wavelength due to compton scattering (in m)\n",
+"LAM=lam+delta_H //wavelength (in m)\n",
+"E=(h*c)/LAM //energy of scattered photon (in J)\n",
+"printf('Energy of scattered photon (in J)=')\n",
+"disp(E)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_15: calculate_number_of_unit_cells.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 15_b_3 , pg 352\n",
+"a=2.88*10^-8 //lattice constant (in cm)\n",
+"d=7200 //density (in Kg/m^3)\n",
+"C=8/a^3 // atomic concentration\n",
+"n=8 //number of atoms/cell\n",
+"n1=C/n //unit cell concentration\n",
+"\n",
+"//since density =7200 Kg/m^3\n",
+"//7200 Kg = 10^6 cc\n",
+"//hence 1Kg = (10^6)/7200 cc\n",
+"N=(n1*10^6)/7200 //number of unit cells present in 1 Kg of metal\n",
+"printf('Number of unit cells present in 1 Kg of metal=')\n",
+"disp(N)\n",
+"printf('unit cells')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_2: find_fundamental_frequency.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 2 , pg 348\n",
+"l=0.7*10^-3//length(in m)\n",
+"E=8.8*10^10//youngs modulus(in N/m^2)\n",
+"d=2800//density(in kg/m^3)\n",
+"p=1//fundamental mode\n",
+"n= p*sqrt(E/d)/(2*l) //natural frequency\n",
+"printf('Fundamental frequency of quartz crystal)\n')\n",
+"printf('n=%.2f Hz',n)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.1_6: calculate_critical_angle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 1) 6 , pg 348\n",
+"n1=1.5 //refractive index of core\n",
+"n2= 1.47 // cladding refractive index\n",
+"theta_c=asin(n2/n1) //critical angle (in radian)\n",
+"printf('critical angle=\n')\n",
+"printf('theta_c=%.2f degree',(theta_c*180)/%pi)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.2_13: calculate_Na_and_acceptance_angle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 2) 13_b , pg 354\n",
+"n1=1.5//core refractive index\n",
+"n2=1.447//cladding refractive index\n",
+"n0=1//refractive index of air\n",
+"NA=sqrt(n1^2-n2^2)//numerical aperture\n",
+"alpha_m =asin(NA/n0)//angle of acceptance (in radian)\n",
+"printf('NA=%.1f \n',NA)\n",
+"printf('alpha_m=%.2f degree\n',(alpha_m*180)/%pi)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.2_1: calculate_the_frequency.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 2) 1 , pg 352\n",
+"l=4*10^-2 //length(in m)\n",
+"E=207 *10^6 //youngs modulus(in N/m^2)\n",
+"d=8900 //density(in kg/m^3)\n",
+"p=1//fundamental mode\n",
+"n= p*sqrt(E/d)/(2*l) //natural frequency\n",
+"printf('Fundamental frequency of quartz crystal)\n')\n",
+"printf('n=%.2f Hz',n)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.2_7: calculate_wavelength_of_scattered_radiation.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 2) 7 , pg 353\n",
+"lam=0.5*10^-9 //wavelength (in m)\n",
+"h=6.625*10^-34//plancksconstant(in J s)\n",
+"c=3*10^8//velocity of x-ray photon(in m/sec)\n",
+"m0=9.11*10^-31//rest mass of electron(in Kg)\n",
+"phi=(45*%pi)/180//angle of scattering (in radian) (converting degree into radian)\n",
+"delta_H=(h*(1-cos(phi)))/(m0*c)//change in wavelength due to compton scattering (in m)\n",
+"LAM=lam+delta_H //wavelength (in m)\n",
+"printf('wavelength of scattered radiation (im m)=')\n",
+"disp(LAM)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.3_11: calculate_mean_free_time.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 3) 11_a , pg 355\n",
+"Un=3*10^-3 //electron mobility (in m^2/(V*s))\n",
+"e=1.6*10^-19 //charge in electron (in C)\n",
+"Me=9.11*10^-31 //mass of electron (in Kg)\n",
+"T=(Me*Un)/e //mean free time\n",
+"printf('Mean free time(in S)')\n",
+"disp(T)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.3_12: calculate_the_resistivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 3) 12_b , pg 356\n",
+"ni=1.5*10^16 //intrinsic carrier density(in m^-3)\n",
+"Un=1.35 //electron mobility (in m^2/(V*s))\n",
+"up=0.48 //hole mobility (in m^2/(V*s))\n",
+"e=1.6*10^-19 //charge in electron (in C)\n",
+"\n",
+"Ix=10^-3 //current (in A)\n",
+"d=100*10^-6 //thickness (in m)\n",
+"Bz=0.1 //magnetic induction (in T)\n",
+"Un1=0.07 //electron mobility (in m^2/(V*s))\n",
+"n=10^23 //doping concentration (in atoms/m^3)\n",
+"\n",
+"sigma=ni*e*(Un+up) // electrical conductivity\n",
+"rho=1/sigma //resistivity\n",
+"Vh=-(Ix*Bz)/(d*e*n) //Hall voltage\n",
+"printf('Resistivity(in ohm*m)')\n",
+"disp(rho)\n",
+"printf('Hall voltage (in V)')\n",
+"disp(Vh)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.3_13: calculate_energy_loss_per_hour_and_intensity_of_magnetization_and_flux_density.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 3) 13_b , pg 357\n",
+"A=250 //area of B-H loop\n",
+"f=50 //frequency (in Hz)\n",
+"d=7.5*10^3 //density (in Kg/m^3)\n",
+"M=10 //mass of core (in Kg)\n",
+"\n",
+"H=2000 //magnetic field intensity (in A/m)\n",
+"Xm=1000 //susceptibility\n",
+"U0=4*%pi*10^-7 // relative permeability\n",
+"\n",
+"V=M/d //volume of sample (in m^3)\n",
+"N=60*60*f //number of cycles per hour\n",
+"EL=A*V*N //energy loss per hour \n",
+"I=H*Xm //intensity of magnetization\n",
+"Ur=1+Xm\n",
+"B=Ur*U0*H //magnetic flux density\n",
+"printf('Energy loss per hour (in J)')\n",
+"disp(EL)\n",
+"printf('Intensity of magnetization (in Wb/m^3)')\n",
+"disp(I)\n",
+"printf('Magnetic flux density(in T)')\n",
+"disp(B)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 13.3_14: find_capacitance_and_electric_flux_density.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"// Additional solved numerical questions , Example(set 3) 14 , pg 358\n",
+"Er1=1.0000684 //Dielectric constant (for sum 14_a_2)\n",
+"N=2.7*10^25 //(in atoms/m^3)\n",
+"E0=8.85*10^-12 //permittivity of free space (in F/m)\n",
+"Er2=6 //dielectric constant (for sum 14_a_3)\n",
+"E=100 //electric field intensity (in V/m) (for sum 14_a_3)\n",
+"A=200*10^-4 //area (in m^2)\n",
+"Er3=3.7 //dielectric constant (for sum 14_b_2)\n",
+"d=10^-3 //thickness (in m)\n",
+"V=300 //electric potential (in V)\n",
+"Alpha_e=(E0*(Er1-1))/N //electronic polarization\n",
+"R=(Alpha_e/(4*%pi*E0))^(1/3) //radius of atom\n",
+"P=E0*(Er2-1)*E //polarization\n",
+"C=(E0*Er3*A)/d //capacitance\n",
+"E1=V/d //electric flux density\n",
+"printf('Electronic polarization (in F*m^2)')\n",
+"disp(Alpha_e)\n",
+"printf('Radius of He atom(in m)')\n",
+"disp(R)\n",
+"printf('polarization(in C/m^2)')\n",
+"disp(P)\n",
+"printf('capacitance(in F)')\n",
+"disp(C)\n",
+"printf('Electric flux density (in V/m)')\n",
+"disp(E1)"
+ ]
+ }
+],
+"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
+}
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