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{
"metadata": {
"name": "",
"signature": "sha256:90fc77a4706b2ba6c4e383a2e0d80f0a572a43d837aa619ea730d827f91d4409"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"3: The Atomic Structure"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.1, Page number 25"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Z=79; #atomic number of gold\n",
"e=1.6*10**-19; #electron charge(C)\n",
"Eo=8.854*10**-12; #absolute permitivity of free space(F/m)\n",
"K=7.68*1.6*10**-13; #kinectic energy(J)\n",
"\n",
"#calculation\n",
"D=(2*Z*e**2)/(4*math.pi*Eo*K); #closest distance of approach(m)\n",
"\n",
"#Result\n",
"print \"The closest distance of approach is\",round(D/1e-14,2),\"*10**-14 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The closest distance of approach is 2.96 *10**-14 m\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.2, Page number 28"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Z=1; #atomic number of hydrogen\n",
"e=1.6*10**-19; #electron charge(C)\n",
"h=6.625*10**-34; #plank's constant(J-s)\n",
"m=9.1*10**-31; #mass of an electron(kg)\n",
"Eo=8.854*10**-12; #absolute permitivity of free space(F/m)\n",
"c=3*10**8; #speed of light(m/s)\n",
"n=1; #ground state\n",
"\n",
"#calculation\n",
"v=9*10**9*(2*math.pi*Z*e**2)/(n*h); #velocity of ground state(m/s)\n",
"r=(Eo*n**2*h**2)/(math.pi*m*e**2); #radius of Bohr orbit in ground state(m)\n",
"t=(2*math.pi*r)/v; #time taken by electron to traverse the bohr first orbit(s)\n",
"R=(m*(e**4))/(8*(Eo**2)*(h**3)*c); #Rhydberg contstant(m^-1)\n",
"#v=v*10**-5;\n",
"#v=math.ceil(v*10**3)/10**3; #rounding off to 3 decimals\n",
"#r=r*10**10;\n",
"#R=R/10**6;\n",
"\n",
"#Result\n",
"print \"velocity of ground state\",round(v/1e+5,2),\"*10^5 m/s\"\n",
"print \"radius of Bohr orbit in ground state\",round(r/1e-10,2),\"*10^-10 m\"\n",
"print \"time taken by electron to traverse the bohr first orbit\",round(t/1e-16,2),\"micro s\"\n",
"print \"Rhydberg constant is\",round(R/1e+6,3),\"*10**6 m^-1\"\n",
"print \"answer for Rhydberg contstant given in the book differs in the 2nd decimal point\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity of ground state 21.85 *10^5 m/s\n",
"radius of Bohr orbit in ground state 0.53 *10^-10 m\n",
"time taken by electron to traverse the bohr first orbit 1.53 micro s\n",
"Rhydberg constant is 10.901 *10**6 m^-1\n",
"answer for Rhydberg contstant given in the book differs in the 2nd decimal point\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.3, Page number 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"B=2.179*10**-16; #constant(J)\n",
"h=6.6*10**-34; #plank's constant(J-s)\n",
"\n",
"#calculation\n",
"E3=-B/3**2; #energy in 3rd orbit(J)\n",
"E2=-B/2**2; #energy in 2nd orbit(J) \n",
"f=(E3-E2)/h; #frequency of radiation(Hz) \n",
"\n",
"#Result\n",
"print \"frequency of radiation\",round(f/1e+16,1),\"*10**16 Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"frequency of radiation 4.6 *10**16 Hz\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.4, Page number 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Z=1; #atomic number of hydrogen\n",
"e=1.6*10**-19; #electron charge(C)\n",
"h=6.625*10**-34; #plank's constant(J-s)\n",
"m=9.1*10**-31; #mass of an electron(kg)\n",
"Eo=8.854*10**-12; #absolute permitivity of free space(F/m)\n",
"n=1; #ground state\n",
"\n",
"#Calculation\n",
"f=(m*Z**2*e**4)/(4*Eo**2*h**3); #frequency(Hz)\n",
"\n",
"#Result\n",
"print \"the frequency is\",round(f/1e+15,2),\"*10**15 Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the frequency is 6.54 *10**15 Hz\n"
]
}
],
"prompt_number": 38
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.5, Page number 30"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"Z=1;\n",
"n=1;\n",
"e=1.6*10**-19; #the charge on electron(C)\n",
"h=6.62*10**-34; #Plank's constant\n",
"Eo=8.854*10**-12; #absolute permitivity of free space(F/m)\n",
"m=9.1*10**-31; #mass of electron(kg)\n",
"\n",
"#calculation\n",
"v=Z*(e**2)/(2*Eo*n*h); #velocity(m/s)\n",
"E=-m*(Z**2)*(e**4)/(8*(Eo*n*h)**2); #energy of hydrogen atom(J)\n",
"f=m*(Z**2)*(e**4)/(4*(Eo**2)*(n*h)**3); #frequecy(Hz)\n",
"\n",
"#Result\n",
"print \"velocity is\",round(v*10**-6,2),\"*10**6 m/s\"\n",
"print \"energy of hydrogen atom\",round(E*10**19,1),\"*10**-19 J\"\n",
"print \"frequecy\",round(f/1e+15,1),\"*10**15 Hz\"\n",
"print \"answer for velocity given in the book is wrong\"\n",
"print \"answer for frequency given in the book varies due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"velocity is 2.18 *10**6 m/s\n",
"energy of hydrogen atom -21.7 *10**-19 J\n",
"frequecy 6.6 *10**15 Hz\n",
"answer for velocity given in the book is wrong\n",
"answer for frequency given in the book varies due to rounding off errors\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.8, Page number 38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"h=6.625*10**-34; #Plank's constant\n",
"c=3*10**8; #speed of light(m/s)\n",
"E1=10.2; #energy(eV)\n",
"E2=12.09; #energy(eV)\n",
"e=1.6*10**-19; #the charge on electron(C)\n",
"\n",
"#calcualtion\n",
"#principal quantum numbers are 2 & 3 respectively\n",
"lamda1=c*h/(E1*e)*10**10; #wavelength for E1(angstrom)\n",
"lamda2=c*h/(E2*e)*10**10; #wavelength for E2(angstrom)\n",
"\n",
"#Result\n",
"print \"wavelength for 10.2 eV is\",int(lamda1),\"angstrom\"\n",
"print \"wavelength for 12.09 eV is\",int(lamda2),\"angstrom\"\n",
"print \"answers given in the book differ due to rounding off errors\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"wavelength for 10.2 eV is 1217 angstrom\n",
"wavelength for 12.09 eV is 1027 angstrom\n",
"answers given in the book differ due to rounding off errors\n"
]
}
],
"prompt_number": 58
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 3.9, Page number 39"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#import modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"R=10967700; #Rydberg constant(m^-1)\n",
"\n",
"#calculation\n",
"long_lamda=4/(3*R); #as n1=1 and n2=2\n",
"long_lamda=long_lamda*10**10; #long wavelength(angstrom)\n",
"short_lamda=1/R; #as n1=1 and n2=infinity\n",
"short_lamda=short_lamda*10**10; #long wavelength(angstrom)\n",
"\n",
"#Result\n",
"print \"Long wavelength is\",round(long_lamda),\"angstrom\"\n",
"print \"Short wavelength is\",round(short_lamda),\"angstrom\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Long wavelength is 1216.0 angstrom\n",
"Short wavelength is 912.0 angstrom\n"
]
}
],
"prompt_number": 62
}
],
"metadata": {}
}
]
}
|
