summaryrefslogtreecommitdiff
path: root/Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb')
-rw-r--r--Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb1123
1 files changed, 1123 insertions, 0 deletions
diff --git a/Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb b/Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb
new file mode 100644
index 0000000..3ca4b2f
--- /dev/null
+++ b/Applied_Physics_ii_by_H_J_Sawant/5-Quantum_Mechanics.ipynb
@@ -0,0 +1,1123 @@
+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 5: Quantum Mechanics"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_1: find_the_energy_of_an_electron_for_different_states.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_1,pg 5-41\n",
+"\n",
+"//En=(n^2*h^2)/(8*m*e*L^2) n=1,2,3,....\n",
+"\n",
+"e=1.6*10^-19 //charge of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"L=2*10^-10 //width\n",
+"\n",
+"E1=h^2/(8*m*e*L^2) //For ground state n=1\n",
+"\n",
+"printf('\nThe energy of an electron in ground state E1 = %.2f eV\n',E1)\n",
+"\n",
+"E2=4*E1 //For first excited state n=2\n",
+"\n",
+"printf('\nThe energy of an electron in ground state E2 = %.2f eV\n',E2)\n",
+"\n",
+"E3=9*E1 //For second excited state n=3\n",
+"\n",
+"printf('\nThe energy of an electron in ground state E3 = %.2f eV\n',E3)\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_2: find_the_ground_state_energy_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_2,pg 5-42\n",
+"\n",
+"//En=(n^2*h^2)/(8*m*e*L^2) n=1,2,3,....\n",
+"\n",
+"//as width 'L' gets double ,the ground state energy becomes one-fourth\n",
+"\n",
+"E=5.6*10^-3 //Ground state energy of an electron\n",
+"\n",
+"E_new=E/4 //width is doubled\n",
+"\n",
+"printf('\nThe new energy of an electron in ground state E = %.4f\n',E_new)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_3: calculate_the_probability_of_finding_the_particle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_3,pg 5_42\n",
+"\n",
+"//for box of width a , the normalised eigen functions are \n",
+"\n",
+"// 'sci = sqrt(2/a)*sin(n*%pi*x/a)'\n",
+"\n",
+"// 'sci_c = sqrt(2/a)*sin(n*%pi*x/a)' complex conjugate \n",
+"\n",
+"//for first excitation \n",
+"\n",
+"n=2\n",
+"\n",
+"//probability of finding the particle is P = integral a/4 to 3a/4 of sci * sci_c\n",
+"\n",
+"//as 'a' is constant width \n",
+"//assume\n",
+"a=1\n",
+"\n",
+"function y=f(x),y= (2/a)*(sin(n*%pi*x/a))^2, // y = sci * sci_c\n",
+"endfunction\n",
+"\n",
+"P=intg(a/4,3*a/4,f)\n",
+"\n",
+"printf('\nThe probability of finding the particle is P = %.1f',P)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_4: find_the_probability_of_finding_the_particle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_4,pg 5_43\n",
+"\n",
+"//probability of finding the particle is P = integral x1 to x2 of sci * sci_c\n",
+"\n",
+"//interval is (0,1/2)\n",
+"\n",
+"x1=0\n",
+"\n",
+"x2=1/2\n",
+"\n",
+"//sci= x*sqrt(3)\n",
+"\n",
+"//complex conjugate is sci_c = x*sqtr(3)\n",
+"\n",
+"function y=f(x),y=(x*sqrt(3))^2, // y = sci * sci_c\n",
+"endfunction\n",
+"\n",
+"P=intg(x1,x2,f)\n",
+"\n",
+"printf('\nThe probability of finding the particle is P = %.3f',P)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_5: find_the_lowest_energy_states.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_5,pg 5-44\n",
+"\n",
+"//for an electron\n",
+"\n",
+"e=1.6*10^-19 //electron charge\n",
+"\n",
+"m_e=9.1*10^-31 //mass of an electron\n",
+"\n",
+"L=10^-9 //width of well\n",
+"\n",
+"h=6.63*10^-34 //Plank's constant\n",
+"\n",
+"//the energy level are given by En = n^2 *h^2/(8*m*L^2)\n",
+"\n",
+"Ee1=(1^2)*(h^2)/(8*m_e*e*(L^2)) //for n = 1\n",
+"\n",
+"Ee2=(2^2)*(h^2)/(8*m_e*e*(L^2)) //for n = 2\n",
+"\n",
+"Ee3=(3^2)*(h^2)/(8*m_e*e*(L^2)) //for n = 3\n",
+"\n",
+"printf('\n FOR AN ELECTRON')\n",
+"printf('\n the lowest three energy states are obtained ')\n",
+"printf('\n for n = 1 Ee1 = %.4f eV',Ee1)\n",
+"printf('\n for n = 2 Ee2 = %.4f eV',Ee2)\n",
+"printf('\n for n = 3 Ee3 = %.4f eV',Ee3)\n",
+"\n",
+"\n",
+"//for the grain of dust \n",
+"\n",
+"m=10^-9 //mass of grain of dust \n",
+"\n",
+"l=10^-4 //width of well\n",
+"\n",
+"E1=(1^2)*(h^2)/(8*m*e*(l^2)) //for n = 1\n",
+"\n",
+"E2=(2^2)*(h^2)/(8*m*e*(l^2)) //for n = 2\n",
+"\n",
+"E3=(3^2)*(h^2)/(8*m*e*(l^2)) //for n = 3\n",
+"\n",
+"printf('\n\n FOR THE GRAIN OF DUST ')\n",
+"printf('\n the lowest three energy states are obtained ')\n",
+"printf('\n for n = 1 E1 = ')\n",
+"disp(E1)\n",
+"printf(' eV')\n",
+"printf('\n for n = 2 E2 = ')\n",
+"disp(E2)\n",
+"printf(' eV')\n",
+"printf('\n for n = 3 E3 = ')\n",
+"disp(E3)\n",
+"printf(' eV')\n",
+""
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_6: calculate_the_width_of_the_well.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_6,pg 1-45\n",
+"\n",
+"E=38 //potential energy \n",
+"\n",
+"e=1.6*10^-19 //charge of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"//the lowest energy of an electron for n=1 is E=h^2/(8*m*e*L^2) \n",
+"\n",
+"L=sqrt(h^2/(8*m*e*E)) //width of the well\n",
+"\n",
+"printf('\nThe width of the well is L =\n')\n",
+"\n",
+"disp(L)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.15_7: calculate_the_energy_and_wavelength_of_the_emitted_photon.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_15_7,pg 1-45\n",
+"\n",
+"e=1.6*10^-19 //charge of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"c=3*10^8 //speed of light in air\n",
+"\n",
+"//The energy eigen values are given by E=(h^2*n^2)/(8*m*e*L^2) \n",
+"\n",
+"L=5*10^-10 //width of potential well\n",
+"\n",
+"//as electron makes a transittion from its n=2 to n=1 energy level\n",
+"\n",
+"E1=(1*h^2)/(8*m*e*L^2) //for n=1\n",
+"\n",
+"E2=(4*h^2)/(8*m*e*L^2) //for n=2\n",
+"\n",
+"E=E2-E1 //The energy of emitted photon\n",
+"\n",
+"printf('\nThe energy of emitted photon is E2-E1 = %.2f eV\n',E)\n",
+"\n",
+"//The energy of photon in terms of wavelength is (h*c)/lam\n",
+"\n",
+"wavelength=(h*c)/(E*e)\n",
+"\n",
+"printf('\nThe wavelength of emitted photon is = %.9f m\n',wavelength)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_10: calculate_the_de_Broglie_wavelength_and_momentum_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_10,pg 5-11\n",
+"\n",
+"V=10*10^3 //Potential difference\n",
+"\n",
+"wavelength=12.27/sqrt(V) // de Broglie wavelength of an eThelectron accelerated through a potential difference of 'V'\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an electron accelerated through a potential difference of V is = %.4f A.\n',wavelength)\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"p=h/(wavelength*10^-10) //The momentum of an electron\n",
+"\n",
+"printf('\nThe momentum of an electron\n')\n",
+"\n",
+"disp(p)\n",
+"\n",
+"printf('kg-meter/sec\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_11: calculate_the_ratio_of_de_Broglie_wavelengths.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_11,pg 5-11\n",
+"\n",
+"//a proton and alpha particle are accelerated by the same potential difference\n",
+"\n",
+"m_p=1.67*10^-27 //mass of proton\n",
+"\n",
+"m_a=4*m_p //mass of alpha particle (assume mass of alpha particle to be 4 times the mass of proton)\n",
+"\n",
+"e=1.6*10^-19 //charge of proton\n",
+"\n",
+"e_a=2*e //charge of an alpha particle\n",
+"\n",
+"h=6.63*10^-34 //plancks constant\n",
+"\n",
+"wavelength_p=h/sqrt(2*m_p*e) //wavelength of proton\n",
+"\n",
+"wavelength_a=h/sqrt(2*m_a*e_a) //wavelength of an alpha particle\n",
+" \n",
+"ratio=wavelength_p/wavelength_a //ratio of the de Broglie wavelengths associated with proton and alpha particle\n",
+"\n",
+"printf('\nthe ratio of wavelengths associated with proton and alpha particle = %.3f\n',ratio)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_12: calculate_the_velocity_and_de_Broglie_wavelength_of_an_alpha_particle.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_12,pg 5-12\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=6.68*10^-27 //mass of alpha particle \n",
+"\n",
+"E=1.6*10^-16 //energy asociated with alpha particle\n",
+"\n",
+"wavelength=h/sqrt(2*m*E)\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an alpha particle\n')\n",
+"\n",
+"disp(wavelength)\n",
+"\n",
+"printf('meter\n')\n",
+"\n",
+"v=h/(m*wavelength) //velocity of an alpha particle\n",
+"\n",
+"printf('\nThe velocity of an alpha particle v = %.2f m/s\n',v)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_13: find_the_de_Broglie_wavelengths_of_photon_and_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_13,pg 5-12\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"c=3*10^8 //velocity of light in air \n",
+"\n",
+"E=1.6*10^-19 //energy of photon\n",
+"\n",
+"wavelength_ph=h*c/E //The energy of photon is E=h*c/lamph\n",
+"\n",
+"printf('\nThe de Broglie wavelength of a photon\n')\n",
+"\n",
+"disp(wavelength_ph)\n",
+"\n",
+"printf('meter\n')\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"wavelength_e=h/sqrt(2*m*E)\n",
+"\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an electron\n')\n",
+"\n",
+"disp(wavelength_e)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_14: find_the_de_Broglie_wavelength_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_14,pg 5-13\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m_0=9.1*10^-31 //rest mass of electron\n",
+"\n",
+"c=3*10^8 //velocity of light in air\n",
+"\n",
+"E=m_0*c^2 //kinetic energy associated with \n",
+"\n",
+"wavelength=h/sqrt(2*m_0*E) //The de broglie wavelength of an electron\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an electron\n')\n",
+"\n",
+"disp(wavelength)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_1: calculate_de_Broglie_wavelength_and_velocity_and_time.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_1,pg 5-5\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=10^-2 //mass of an moving object\n",
+"\n",
+"v1=1 //velocity of that object\n",
+"\n",
+"wavelength_1=h/(m*v1)\n",
+"\n",
+"printf('\nThe de Broglie Wavelength is\n')\n",
+"\n",
+"disp(wavelength_1)\n",
+"\n",
+"printf('meter\n')\n",
+"\n",
+"wavelength_2=10^-10 //new de Broglie wavelength\n",
+"\n",
+"v2=h/(m*wavelength_2) //new velocity of an object \n",
+"\n",
+"printf('\nThe new velocity of an object is\n')\n",
+"\n",
+"disp(v2)\n",
+"\n",
+"printf('meter/sec\n')\n",
+"\n",
+"d=10^-3 //Distance travelled with speed v2\n",
+"\n",
+"t=(d/v2)/(365*24*60*60) //time required to travel distance\n",
+"\n",
+"printf('\nTime required to travel distance is\n')\n",
+"\n",
+"disp(t)\n",
+"\n",
+"printf('years\n')\n",
+"\n",
+"//mistake in textbook"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_2: calculate_the_velocity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_2,pg 5-6\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"wavelength=10^-10 //de Broglie wavelength of an electron\n",
+"\n",
+"v=h/(m*wavelength) //velocity of an electron\n",
+"\n",
+"printf('\nThe velocity of an electron is v = %.1f m/s\n',v)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_3: calculate_kinetic_energy_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_3,pg 5-6\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"wavelength=5000*10^-10 //de Broglie wavelength of an electron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"E=h^2/(2*m*wavelength^2*e) //Kinetic energy of an electron \n",
+"\n",
+"printf('\nKinetic energy of an electron is E = %.9f eV\n',E)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_4: find_the_wavelength_of_a_beam_of_neutron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_4,pg 5-7\n",
+"\n",
+"E=0.025 //energy of neutron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=1.676*10^-27 //mass of a neutron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"wavelength=h/sqrt(2*m*E*e) //The Wavelength of a beam of neutron\n",
+"\n",
+"printf('\nThe Wavelength of a beam of neutron is\n')\n",
+"\n",
+"disp(wavelength)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_5: find_the_de_Broglie_wavelength_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_5,pg 5-7\n",
+"\n",
+"E=120 //kinetic energy of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"wavelength=h/sqrt(2*m*E*e) //The de Broglie Wavelength of an electron\n",
+"\n",
+"printf('\nThe de Broglie Wavelength of an electron is\n')\n",
+"\n",
+"disp(wavelength)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_6: calculate_the_velocity_and_kinetic_energy_of_neutron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_6,pg 5-7\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=1.67*10^-27 //mass of a neutron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"wavelength=10^-10 //The de Broglie Wavelength of a neutron\n",
+"\n",
+"v=h/(m*wavelength) //velocity of a neutron\n",
+"\n",
+"printf('\nThe velocity of a neutron is v= %.f m/s\n',v)\n",
+"\n",
+"E=h^2/(2*m*wavelength^2*e) //Kinetic energy of a neutron\n",
+"\n",
+"printf('\nKinetic energy of a neutron is E= %.5f eV\n',E)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_7: find_the_de_Broglie_wavelength.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_7,pg 5-8\n",
+"\n",
+"//(1)\n",
+"V=182 //Potential difference \n",
+"\n",
+"wavelength_1=12.27*10^-10/sqrt(V) //The de Broglie wavelength of an electron accelerated through a potential diff. of 'V'\n",
+"\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an electron accelerated through a potential diff. of V is\n')\n",
+"\n",
+"disp(wavelength_1)\n",
+"\n",
+"printf('meter\n')\n",
+"\n",
+"//(2)\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=1\n",
+"\n",
+"v=1\n",
+"\n",
+"wavelength_2=h/(m*v)\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an object is\n')\n",
+"\n",
+"disp(wavelength_2)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_8: find_the_momentum_and_energy_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_8,pg 5-9\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"e=1.6*10^-19 //charge on electron\n",
+"\n",
+"wavelength=10^-14 //The de Broglie wavelength of an electron\n",
+"\n",
+"p=h/wavelength //as the de Broglie wavelength of an electron is (lam=h/p)\n",
+"\n",
+"printf('\nThe momentum of an electron is\n')\n",
+"\n",
+"disp(p)\n",
+"\n",
+"printf('kg-meter/sec\n')\n",
+"\n",
+"E=p^2/(2*m*e)*10^-6 //energy corresponds to momentum\n",
+"\n",
+"printf('\nenergy of an electron is E = %.2f MeV\n',E)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.3_9: find_the_parameters_for_an_electron_wave.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_3_9,pg 5-10\n",
+"\n",
+"V=3000 //Potential difference \n",
+"\n",
+"wavelength=12.27/sqrt(V) //The de Broglie wavelength of an electron accelerated through a potential diff. of 'V'\n",
+"\n",
+"printf('\nThe de Broglie wavelength of an electron accelerated through a potential diff. of V is %.3f A.\n',wavelength)\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"p=h/(wavelength*10^-10) //as the de Broglie wavelength of an electron is (wavelength=h/p)\n",
+"\n",
+"printf('\nThe momentum of an electron is\n')\n",
+"\n",
+"disp(p)\n",
+"\n",
+"printf('kg-meter/sec\n')\n",
+"\n",
+"wave_no=1/(wavelength*10^-10) //wave number \n",
+"\n",
+"printf('\nThe wave number = %.f/m\n',wave_no)\n",
+"\n",
+"d=2.04 //distance between planes\n",
+"\n",
+"n=1 //For first ordet reflection\n",
+"\n",
+"angle=asind(n*wavelength/(2*d)) //By Bragg's law '2dsin(angle)=n*wavelength' \n",
+"\n",
+"printf('\nThe Bragg angle = %.3f Degree\n',angle)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_1: find_the_accuracy_in_position_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_1,pg 5-26\n",
+"\n",
+"unc=1*10^-4 //as uncertainty is 0.01%\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"v=400 //speed of an electron\n",
+"\n",
+"delta_v=unc*v //error in measurement of speed \n",
+"\n",
+"delta_x=h/(4*%pi*m*delta_v) //By Heisenberg's uncertainty priciple\n",
+"\n",
+"printf('\nThe accuracy in position of an electron Delta_x = %.5f m\n',delta_x)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_2: calculate_the_percentage_of_uncertainty.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_2,pg 5-27\n",
+"\n",
+"delta_x=10*10^-9 //position is located within this distance\n",
+"\n",
+"h=6.63*10^-34 //plancks constant\n",
+"\n",
+"delta_px=h/(4*%pi*delta_x) //By Heisenberg's uncertainty priciple\n",
+"\n",
+"E=1.6*10^-16 //Energy associated with an electron\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"p=sqrt(2*m*E) //momentum of an electron\n",
+"\n",
+"percentage=delta_px*100/p //percentage uncertainty in momentum\n",
+"\n",
+"printf('\npercentage uncertainty in momentum of an electron = %.4f \n',percentage)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_3: find_the_accuracy_in_position_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_3,pg 5-27\n",
+"\n",
+"\n",
+"uncertainty=1*10^-4 //as uncertainty is 0.01%\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"v=4*10^5 //speed of an electron\n",
+"\n",
+"delta_v=uncertainty*v //error in measurement of speed \n",
+"\n",
+"delta_x=h/(4*%pi*m*delta_v) //By Heisenberg's uncertainty priciple\n",
+"\n",
+"printf('\nThe accuracy in position of an electron Delta_x = %.8f m\n',delta_x)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_4: find_the_accuracy_in_position_of_an_electron.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_4,pg 5-27\n",
+"\n",
+"uncertainty=1*10^-2 //as uncertainty is 1%\n",
+"\n",
+"m=9.1*10^-31 //mass of an electron\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"v=1.88*10^6 //speed of an electron\n",
+"\n",
+"delta_v=uncertainty*v //error in measurement of speed \n",
+"\n",
+"delta_x=h/(4*%pi*m*delta_v) //By Heisenberg's uncertainty priciple\n",
+"\n",
+"printf('\nThe accuracy in position of an electron Delta_x =\n')\n",
+"\n",
+"disp(delta_x)\n",
+"\n",
+"printf('meter\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_5: calculate_the_minimum_time_spent_by_the_electrons.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_5,pg 5-28\n",
+"\n",
+"//By Heisenberg's uncertainty principle\n",
+"\n",
+"//(delta_E*delta_t)>=h/(4*%pi)\n",
+"\n",
+"//therefore (h*c*delta_wavelength*delta_t/wavelength^2) >= h/(4*%pi)\n",
+"\n",
+"wavelength=4*10^-7 //wavelength of spectral line\n",
+"\n",
+"c=3*10^8 //velocity of light in air\n",
+"\n",
+"delta_wavelength=8*10^-15 //width of spectral line\n",
+"\n",
+"delta_t=wavelength^2/(4*%pi*c*delta_wavelength)\n",
+"\n",
+"printf('\nThe minimum time required by the electrons in upper energy state Delta_t = \n')\n",
+"\n",
+"disp(delta_t)\n",
+"\n",
+"printf('sec\n')"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_6: calculate_the_uncertainty_in_energy.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_6,pg 5-29\n",
+"\n",
+"h=6.63*10^-34 //Plancks constant\n",
+"\n",
+"e=1.6*10^-19 //charge of an electron\n",
+"\n",
+"delta_t=1.4*10^-10 //time spent in excited state\n",
+"\n",
+"delta_E=h/(4*%pi*delta_t*e) //By Heisenberg's uncertainty principle (delta_E*delta_t)>= h/(4*%pi)\n",
+"\n",
+"printf('\nThe uncertainty in energy of Iradium in the excited state Delta_E = %.8f eV\n',delta_E)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 5.7_7: find_the_time_spent_by_an_atom_in_excited_state.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Chapter-5,Example5_7_7,pg 5-29\n",
+"\n",
+"//By Heisenberg's uncertainty principle\n",
+"\n",
+"//(delta_E*delta_t)>=h/(4*%pi)\n",
+"\n",
+"//therefore (h*c*delta_wavelength*delta_t/wavelength^2) >= h/(4*%pi)\n",
+"\n",
+"wavelength=546*10^-9 //wavelength of spectral line\n",
+"\n",
+"c=3*10^8 //velocity of light in air\n",
+"\n",
+"delta_wavelength=10^-14 //width of spectral line\n",
+"\n",
+"delta_t=wavelength^2/(4*%pi*c*delta_wavelength)\n",
+"\n",
+"printf('\nThe time spent by an atom in the excited state \n')\n",
+"\n",
+"disp(delta_t)\n",
+"\n",
+"printf('sec\n')"
+ ]
+ }
+],
+"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
+}
generated by cgit (git 2.34.1) at 2025-01-08 23:27:43 +0000