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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#4: Principles of quantum mechanics"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.1, Page number 4.30"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"wavelength is 0.0275 nm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"E=2000; #energy(eV)\n",
"\n",
"#Calculation\n",
"lamda=h/math.sqrt(2*m*E*e); #wavelength(m)\n",
"\n",
"#Result\n",
"print \"wavelength is\",round(lamda*10**9,4),\"nm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.2, Page number 4.30"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"velocity is 438.6 *10**4 m/s\n",
"answer varies due to rounding off errors\n",
"kinetic energy is 54.71 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.626*10**-34; #planck's constant\n",
"lamda=1.66*10**-10; #wavelength(m)\n",
"\n",
"#Calculation\n",
"v=h/(m*lamda); #velocity(m/s)\n",
"E=h**2/(2*m*e*lamda**2); #kinetic energy(eV)\n",
"\n",
"#Result\n",
"print \"velocity is\",round(v/10**4,1),\"*10**4 m/s\"\n",
"print \"answer varies due to rounding off errors\"\n",
"print \"kinetic energy is\",round(E,2),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.3, Page number 4.31"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"energy value in ground state is 37.7377 eV\n",
"energy value in 1st state is 150.95 eV\n",
"energy value in 2nd state is 339.6395 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=1*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"E2=4*E1; #energy value in 1st state(eV)\n",
"E3=9*E1; #energy value in 2nd state(eV)\n",
"\n",
"#Result\n",
"print \"energy value in ground state is\",round(E1,4),\"eV\"\n",
"print \"energy value in 1st state is\",round(E2,2),\"eV\"\n",
"print \"energy value in 2nd state is\",round(E3,4),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.4, Page number 4.31"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"minimum energy is 2.3586 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=4*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"\n",
"#Result\n",
"print \"minimum energy is\",round(E1,4),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.5, Page number 4.32"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"wavelength is 0.01 nm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=15*10**3; #voltage(V)\n",
"\n",
"#Calculation\n",
"lamda=1.227/math.sqrt(V); #wavelength(nm)\n",
"\n",
"#Result\n",
"print \"wavelength is\",round(lamda,2),\"nm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.6, Page number 4.32"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"minimum energy is 150.95 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=0.05*10**-9; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"\n",
"#Result\n",
"print \"minimum energy is\",round(E1,2),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.8, Page number 4.32"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"minimum energy is 4.2 eV\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=3*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"\n",
"#Result\n",
"print \"minimum energy is\",round(E1,1),\"eV\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.9, Page number 4.33"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"de broglie wavelength is 8488 nm\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"me=1.676*10**-27; #mass(kg) \n",
"mn=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"\n",
"#Calculation\n",
"lamda_n=h/math.sqrt(4*mn*me); #de broglie wavelength(m)\n",
"\n",
"#Result\n",
"print \"de broglie wavelength is\",int(lamda_n*10**9),\"nm\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.10, Page number 4.33"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"energy value in 2nd quantum state is 37.738 eV\n",
"energy value in 4th quantum state is 150.95 eV\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=2*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"E2=2**2*E1; #energy value in 2nd quantum state(eV)\n",
"E4=4**2*E1; #energy value in 2nd quantum state(eV)\n",
"\n",
"#Result\n",
"print \"energy value in 2nd quantum state is\",round(E2,3),\"eV\"\n",
"print \"energy value in 4th quantum state is\",round(E4,2),\"eV\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.11, Page number 4.34"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"interplanar spacing is 0.382 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"e=1.6*10**-19; \n",
"m=9.1*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"V=344; #potemtial(V)\n",
"n=1;\n",
"theta=60; #angle(degrees)\n",
"\n",
"#Calculation\n",
"theta=theta*math.pi/180; #angle(radian)\n",
"d=n*h/(2*math.sin(theta)*math.sqrt(2*m*V*e)); #interplanar spacing(m)\n",
"\n",
"#Result\n",
"print \"interplanar spacing is\",round(d*10**10,3),\"angstrom\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.12, Page number 4.34"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"energy required to pump an electron is 301.57 eV\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.11*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=1*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"E3=3**2*E1; #energy value in 2nd quantum state(eV)\n",
"E=E3-E1; #energy required to pump an electron(eV)\n",
"\n",
"#Result\n",
"print \"energy required to pump an electron is\",round(E,2),\"eV\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.13, Page number 4.34"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"minimum energy is 9.424 eV\n",
"answer varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"n=1;\n",
"e=1.6*10**-19; \n",
"m=9.11*10**-31; #mass(kg)\n",
"h=6.63*10**-34; #planck's constant\n",
"L=2*10**-10; #width(m)\n",
"\n",
"#Calculation\n",
"E1=n**2*h**2/(8*m*e*L**2); #energy value in ground state(eV)\n",
"\n",
"#Result\n",
"print \"minimum energy is\",round(E1,3),\"eV\"\n",
"print \"answer varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.14, Page number 4.35"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"wavelength is 0.31 angstrom\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"V=1600; #voltage(V)\n",
"\n",
"#Calculation\n",
"lamda=1.227/math.sqrt(V); #wavelength(nm)\n",
"\n",
"#Result\n",
"print \"wavelength is\",round(lamda*10,2),\"angstrom\""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
|
