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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2:Atomic Spectra-II"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:4,Page no:460"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"rP = 4 \n",
"rD = 5 \n",
"LP = 1 \n",
"LP = 2 \n",
"jP = (5/2.0, 3/2.0, 1/2.0) \n",
"jD = (4, 3, 2, 1)\n",
"\n",
"#Calculation\n",
"import math\n",
"SP = (rP-1)/2.0 \n",
"SD = (rD-1)/2.0 \n",
"i=0 \n",
"JP=[0,0,0]\n",
"JD=[0,0,0,0,0]\n",
"for i in range(0,3):\n",
" JP[i] =round(math.sqrt(jP[i]*(jP[i])+1) ,2)\n",
"i=0 \n",
"for i in range(0,4):\n",
" JD[i] = round(math.sqrt(jD[i]*(jD[i]+1)) ,2)\n",
" \n",
"#Result\n",
"print\"\\nAngular moments allowed for 4P :\",JP\n",
"print\"\\nAngular moments allowed for 5D : \",JD\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Angular moments allowed for 4P : [2.69, 1.8, 1.12]\n",
"\n",
"Angular moments allowed for 5D : [4.47, 3.46, 2.45, 1.41, 0]\n"
]
}
],
"prompt_number": 80
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:9,Page no:462"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"l=1\n",
"s=1/2.0\n",
"j=3/2.0\n",
"\n",
"#calculation\n",
"import math\n",
"angle=((j*(j+1))-(l*(l+1))-(s*(s+1)))/(2*math.sqrt(l*s*(l+1)*(s+1))) #value of cos \u03b8\n",
"\n",
"#Result\n",
"print\"\\n cos \u03b8 = \",round(angle,3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" cos \u03b8 = 0.408\n"
]
}
],
"prompt_number": 81
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:10,Page no:462"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"e=1.6*10**-19 #charge of electron (C)\n",
"m=9.1*10**-31 #mass of electron (kg)\n",
"B=0.1 #external magnetic field (Wb/m**2)\n",
"g=4/3.0\n",
"mu=9.27*10**-24 #(J/T)\n",
"\n",
"#calculation\n",
"from sympy import *\n",
"mu_b=Symbol(\"\u00b5b\")\n",
"import math\n",
"E=round(g*B,3)*mu_b #The spacing of adjacent sub-levels (J)\n",
"v=(e*B)/(4*math.pi*m) #Larmor frequency (Hz)\n",
"\n",
"#Result\n",
"print\"\\n The spacing of adjacent sub-levels =\",E,\"J\\n Larmor frequency =%.1e\"%v,\"Hz\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" The spacing of adjacent sub-levels = 0.133*\u00b5b J\n",
" Larmor frequency =1.4e+09 Hz\n"
]
}
],
"prompt_number": 82
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:11,Page no:462"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"mu=9.27*10**-24 #(J/T)\n",
"g=2 \n",
"ms=1/2.0 \n",
"dB=2*10**2 #gradient of magnetic field (T/m)\n",
"m=1.67*10**-27 #maas of hydrogen atom (kg)\n",
"l=0.2 #distance travelled by hydrogen atom (m)\n",
"v=2*10**5 #speed of hydrogen atom (m/s)\n",
"\n",
"#calculation\n",
"muz=g*mu*ms #Resolved part of magnetic moment in the direction of magnetic field (J/T)\n",
"Fz=muz*dB #Force on the atom (N)\n",
"z=0.5*(Fz/m)*(l/v)**2 #Displacement of beam (m)\n",
"sep=2*z #Total separation (m)\n",
"\n",
"#Result\n",
"print\"\\n Total separation =%.2e\"%sep,\"m\" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" Total separation =1.11e-06 m\n"
]
}
],
"prompt_number": 83
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:12,Page no:463"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"l=1.0\n",
"s=1.0/2.0\n",
"j1=1.0/2.0\n",
"j2=3.0/2.0\n",
"\n",
"#calculation\n",
"import math\n",
"L=math.sqrt(l*(l+1.0)) #orbital angular momenta\n",
"S=math.sqrt(s*(s+1.0)) #spin angular momenta\n",
"J1=math.sqrt(j1*(j1+1.0)) #total angular momenta\n",
"J2=math.sqrt(j2*(j2+1.0)) #total angular momenta\n",
"theta1=(180.0/math.pi)*math.acos(((j2*(j2+1))-(l*(l+1))-(s*(s+1)))/(2.0*math.sqrt(l*(l+1.0))*math.sqrt(s*(s+1)))) #angle b/w l and s (degree)\n",
"theta2=(180.0/math.pi)*math.acos(((j1*(j1+1))-(l*(l+1))-(s*(s+1)))/(2.0*math.sqrt(l*(l+1.0))*math.sqrt(s*(s+1)))) #angle b/w l and s (degree)\n",
"#Result\n",
"print\"\\n |l| =\",round(L,2),\"*h=\u221a2h\\n |s| =\",round(S,2),\"*h=\u221a3/4 h\\n |j| =\",round(J1,2),\"*h=\u221a3/4 h,\",round(J2,2),\"*h=\u221a15/4 h\\n \u03b81 =%d\"%theta1,\"\u02da\\n \u03b82 =%d\"%round(theta2),\"\u02da\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" |l| = 1.41 *h=\u221a2h\n",
" |s| = 0.87 *h=\u221a3/4 h\n",
" |j| = 0.87 *h=\u221a3/4 h, 1.94 *h=\u221a15/4 h\n",
" \u03b81 =65 \u02da\n",
" \u03b82 =145 \u02da\n"
]
}
],
"prompt_number": 84
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:13,Page no:463"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"B=0.5 #magnetic field (T)\n",
"s=1/2.0 \n",
"g=2 \n",
"\n",
"#calculation\n",
"import math\n",
"from sympy import *\n",
"mu_B=Symbol(\"\u03bc\u03b2\")\n",
"S=math.sqrt(s*(s+1)) #Magnitude of spin vector\n",
"theta1=(180.0/math.pi)*math.acos(0.5/S) #Orientation of spin vector (degree)\n",
"theta2=(180.0/math.pi)*math.acos(-0.5/S) #Orientation of spin vector (degree)\n",
"E=2*g*mu_B*B #Separation of the energy levels (in terms of \u03bc\u03b2)\n",
"\n",
"#Result\n",
"print\"\u03b8 =\",round(theta1,1),\"\u02da and \u03b8=\",round(theta2,1),\"\u02da\\n \u0394E =\",E\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" \u03b8 = 54.7 \u02da and \u03b8= 125.3 \u02da\n",
" \u0394E = 2.0*\u03bc\u03b2\n"
]
}
],
"prompt_number": 77
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:15,Page no:464"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"zH=1.0 #atomic no. of H\n",
"zHe=2.0 #atomic no. of He\n",
"deltaHe=5.84 #doublet splitting of the first excited state of He (cm-1)\n",
"\n",
"#calculation\n",
"deltaH=deltaHe*(zH/zHe)**4 #doublet splitting for hydrogen atom (cm-1)\n",
"\n",
"#Result\n",
"print\"Doublet splitting for H atom =\",deltaH,\"cm**-1\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Doublet splitting for H atom = 0.365 cm**-1\n"
]
}
],
"prompt_number": 78
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example no:16,Page no:464"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"z=1 #atomic no. of hydrogen atom\n",
"n=2\n",
"l=1\n",
"\n",
"#calculation\n",
"delta=(5.84*z**4)/(n**3*l*(l+1)) #spin-orbit interaction splitting (cm-1)\n",
"\n",
"#Result\n",
"print\"Spin-orbit interaction splitting =\",delta,\"cm**-1\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Spin-orbit interaction splitting = 0.365 cm**-1\n"
]
}
],
"prompt_number": 20
}
],
"metadata": {}
}
]
}
|
