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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 1:Atomic Spectra-I"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:1,Page no:405"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"z=2 #atomic no. of He\n",
"a0=0.529 #radius of first Bohr orbit of H atom (\u00c5)\n",
"n=1 #no. of Bohr orbit\n",
"A=2.19*10**6 #velocity of e in first Bohr orbit of H atom (m/s)\n",
"B=4.14*10**15 #orbital frequency in the first Bohr orbit of H atom (rad/s)\n",
"E0=13.6 #energy of electron in ground state of H atom (eV)\n",
"n1=1 \n",
"n2=2 \n",
"R=1.097*10**7 #Rydberg constant (m-1)\n",
"\n",
"#Calculation\n",
"#(i) radius of first Bohr orbit\n",
"r=a0/2.0 #radius of first Bohr orbit (\u00c5)\n",
"#(ii) velocity of electron in the first orbit\n",
"v=A*(z/n) #velocity of electron in the first orbit (m/s)\n",
"#(iii) orbital frequency in the first orbit\n",
"omega=B*(z**2/n**3) #orbital frequency in the first orbit (rad/s)\n",
"#(iv) kinetic and binding energy\n",
"KE=E0*(z**2/n**2) #kinetic energy of electron in the ground state (eV)\n",
"BE=KE #binding energy of electron in the ground state (eV)\n",
"#(v) ionization potential and first excitation potential\n",
"IP=KE #ionization potential (eV)\n",
"EE=E0*z**2*((1.0/n1**2)-(1.0/n2**2)) #first excitation potential (eV)\n",
"#(vi) wavelength of the resonance line emitted in the transition n=2 to n=1\n",
"lembda=(1.0/(R*z**2*((1.0/n1**2)-(1.0/n2**2))))*10**10 #wavelength of the resonance line emitted in the transition n=2 to n=1 (\u00c5)\n",
"\n",
"#Result\n",
"print\"\\n(i) radius =\",round(r,3),\"\u00c5\"\n",
"print\"(ii) velocity =%.2e\"%v,\"m/s\"\n",
"print\"(iii) orbital frequency =\",omega,\"rad/s\"\n",
"print\"(iv) Kinetic energy =\",KE,\"eV Binding energy =\",BE,\"eV\"\n",
"print\"(v) Ionization potential =\",IP,\"eV EE =\",EE,\"eV\"\n",
"print\"(vi) wavelength =\",lembda,\"\u00c5\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"(i) radius = 0.265 \u00c5\n",
"(ii) velocity =4.38e+06 m/s\n",
"(iii) orbital frequency = 1.656e+16 rad/s\n",
"(iv) Kinetic energy = 54.4 eV Binding energy = 54.4 eV\n",
"(v) Ionization potential = 54.4 eV EE = 40.8 eV\n",
"(vi) wavelength = 303.85900942 \u00c5\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:2,Page no:406"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"z=1 #atomic no. of H atom\n",
"m=1.68*10**-27 #mass of H atom (kg)\n",
"h=1.054*10**-34 #Planck's constant (joule second)\n",
"R=10967800 #Rydberg constant (m-1)\n",
"e=1.6*10**-19 #Charge of electron (coulombs)\n",
"c=3*10**8 #speed of light (m/s)\n",
"\n",
"#Calculation\n",
"import math\n",
"#(i) recoil velocity\n",
"v=(3*math.pi*h*R*z**2)/(2*m) #recoil velocity of H atom (m/s)\n",
"#(ii) recoil kinetic energy\n",
"Er=(9/8.0)*((math.pi*h*R*z**2)**2/(m*e)) #recoil kinetic energy of H atom (eV)\n",
"#(iii) energy of emitted photon\n",
"E=(1.5*math.pi*h*c*R*z**2)/e #energy of emitted photon (eV)\n",
"\n",
"#Result\n",
"print\"(i) recoil velocity =\",round(v,2),\"m/s\"\n",
"print\"(ii) recoil kinetic energy =%.1e\"%Er,\"eV\"\n",
"print\"(iii) energy of emitted photon =\",round(E,2),\"eV\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(i) recoil velocity = 3.24 m/s\n",
"(ii) recoil kinetic energy =5.5e-08 eV\n",
"(iii) energy of emitted photon = 10.21 eV\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:3,Page no:407"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"z=2 #atomic no. of He atom\n",
"h=1.054*10**-34 #Planck's constant (joule second)\n",
"R=10967800 #Rydberg constant (m-1)\n",
"e=1.6*10**-19 #Charge of electron (coulombs)\n",
"c=3*10**8 #speed of light (m/s)\n",
"\n",
"#calculation\n",
"E=1.5*math.pi*h*c*R*z**2 #The energy of the emitted photon (J)\n",
"IE=2*math.pi*h*c*R #Ionization energy of H atom (J)\n",
"KE=(E-IE)/e #Kinetic energy of the photoelectron (eV)\n",
"\n",
"#Result\n",
"print\"\\nKinetic energy of photoelectron =\",round(KE,1),\"eV\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Kinetic energy of photoelectron = 27.2 eV\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:4,Page no:407"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"ratio=4 #ratio of wavelengths\n",
"z1=1 #atomic no. of hydrogen atom\n",
"\n",
"#calculation\n",
"z2=math.sqrt(ratio*z1**2) #atomic no. of unknown element\n",
"\n",
"#Result\n",
"print\"Atomic no. =\",z2,\"(helium)\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Atomic no. = 2.0 (helium)\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:5,Page no:407"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"lembda1=108.5*10**-9 #wavelength (m)\n",
"lembda2=30.4*10**-9 #wavelength (m)\n",
"R=1.097*10**7 #Rydberg constant (m-1)\n",
"z=2 #atomic no. of He\n",
"n0=1 #ground state\n",
"\n",
"#calculation\n",
"import math\n",
"n=math.sqrt(1.0/((1.0/n0**2)-(((1.0/lembda1)+(1.0/lembda2))/(R*z**2)))) #quantum no. corresponding to the excited state of He+\n",
"\n",
"#Result\n",
"print\"n =\",round(n )\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"n = 5.0\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:6,Page no:408"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"z=2 #atomic no. of He+ ion\n",
"lembda=133.7*10**-9 #difference b/w the first lines of the Balmer and Lyman series (m)\n",
"n1=1\n",
"n2=2\n",
"n3=3\n",
"\n",
"#calculation\n",
"R=(1.0/(lembda*z**2))*((1.0/((1.0/n2**2)-(1.0/n3**2)))-(1.0/((1.0/n1**2)-(1.0/n2**2)))) #Rudberg constant (m-1)\n",
"\n",
"#Result\n",
"print\"R =%.3e\"%R,\"m**-1\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"R =1.097e+07 m**-1\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:7,Page no:409"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R=1.097*10**7 #Rydberg constant (m-1)\n",
"lembda=59.3*10**-9 #wavelength difference b/w first lines of Balmer and Lyman series (m)\n",
"\n",
"#calculation\n",
"import math\n",
"z=math.sqrt(88.0/(15.0*R*lembda)) #atomic no.\n",
"\n",
"#Result\n",
"print\"Z =\",round(z)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Z = 3.0\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:8,Page no:409"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R=1.097*10**7 #Rydberg constant (m-1)\n",
"ratio=1836 #ratio of maas of tritium and hydrogen\n",
"\n",
"#calculation\n",
"lembda=(36*2*10**10)/(5*R*3*ratio) #separation of the first line of the Balmer series (\u00c5)\n",
"\n",
"#Result\n",
"print\"\u0394\u03bb =\",round(lembda,1),\"\u00c5\" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\u0394\u03bb = 2.4 \u00c5\n"
]
}
],
"prompt_number": 22
}
],
"metadata": {}
}
]
}
|
