{
"metadata": {
"name": "Chapter6",
"signature": "sha256:36f31f6870acf2c11b00274dcf34bd9e9879abf6f82026373900139ccc4b5799"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6:The Rutherford Bohr Model"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1 Page 178"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sqrt, pi\n",
"R=0.1;Z=79.0; x=1.44; #x=e^2/4*pi*epsi0\n",
"zkR2=2*Z*x/R # from zkR2= (2*Z*e^2)*R^2/(4*pi*epsi0)*R^3\n",
"mv2=10.0*10**6; #MeV=>eV\n",
"\n",
"#calculation\n",
"theta=sqrt(3.0/4)*zkR2/mv2; #deflection angle\n",
"theta=theta*(180/pi); #converting to degrees\n",
"\n",
"#result\n",
"print\"Hence the average deflection angle per collision in degrees is\",round(theta,3 );"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Hence the average deflection angle per collision in degrees.is 0.011\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2 Page 181"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sin, cos, tan, sqrt, pi\n",
"Na=6.023*10**23;p=19.3;M=197.0;\n",
"n=Na*p/M; #The number of nuclei per atom\n",
"t=2*10**-6;Z=79;K=8*10**6;x=1.44; theta=90.0*pi/180; #x=e^2/4*pi*epsi0\n",
"b1=t*Z*x/tan(theta/2)/(2*K) #impact parameter b\n",
"f1=n*pi*b1**2*t #scattering angle greater than 90\n",
"\n",
"#result\n",
"print\"The fraction of alpha particles scattered at angles greater than 90 degrees is %.1e\" %f1;\n",
"\n",
"#part b\n",
"theta=45.0*pi/180;\n",
"b2=t*Z*x/tan(theta/2)/(2*K);\n",
"f2=n*pi*b2**2*t; #scattering angle greater than 45\n",
"fb=f2-f1 #scattering angle between 45 to 90\n",
"\n",
"#result\n",
"print\"The fraction of particles with scattering angle from 45 to 90 is %.1e\" %fb;"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The fraction of alpha particles scattered at angles greater than 90 degrees is 7.5e-05\n",
"The fraction of particles with scattering angle from 45 to 90 is 3.6e-04\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3 Page 185"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from math import sin, cos, tan, sqrt, pi\n",
"Z=79.0;x=1.44;K=8.0*10**6;z=2; #where x=e^2/4*pi*epsi0;z=2 for alpha particles\n",
"\n",
"#calculation\n",
"d=z*x*Z/K; #distance\n",
"\n",
"#result\n",
"print \"The distance of closest approach in nm. is\",d*10**-9"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The distance of closest approasch in nm. is 2.844e-14\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4 Page 188"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"sl=820.1;n0=3.0; #given values\n",
"n=4;w=sl*(n**2/(n**2-n0**2)); \n",
"#result\n",
"print \"The 3 longest possible wavelengths in nm respectively are a.\",round(w,3),; \n",
"\n",
"#partb\n",
"n=5.0;w=sl*(n**2/(n**2-n0**2)); \n",
"\n",
"#result\n",
"print \"b. (in nm)\",round(w,3),;\n",
"\n",
"#partc\n",
"n=6.0;w=sl*(n**2/(n**2-n0**2));\n",
"\n",
"#result\n",
"print \"c. (in nm )\",round(w,3);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The 3 longest possible wavelengths in nm respectively are a. 1874.514 b. (in nm) 1281.406 c. (in nm ) 1093.467\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5 Page 189"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"sl=364.5;n=3.0; #given variables and various constants are declared in the subsequent steps wherever necessary \n",
"w1=sl*(n**2/(n**2-4)); #longest wavelength of balmer \n",
"c=3.0*10**8;\n",
"f1=c/(w1*10**-9); #corresponding freq.\n",
"n0=1.0;n=2.0; \n",
"\n",
"#calculation\n",
"w2=91.13*(n**2/(n**2-n0**2)); #first longest of lymann \n",
"f2=c/(w2*10**-9); #correspoding freq\n",
"n0=1.0;n=3.0\n",
"w3=91.13*(n**2/(n**2-n0**2)); #second longest of lymann\n",
"f3=3.0*10**8/(w3*10**-9) #corresponding freq.\n",
"\n",
"#result\n",
"print \"The freq. corresponding to the longest wavelength of balmer is %.1e\" %f1,\" & First longest wavelength of Lymann is %.1e\" %f2;\n",
"print\"The sum of which s equal to %.1e\" %(f1+f2);\n",
"print\"The freq. corresponding to 2nd longest wavelength was found out to be %.1e\" %f3,\"Hence Ritz combination principle is satisfied.\";"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The freq. corresponding to the longest wavelength of balmer is 4.6e+14 & First longest wavelength of Lymann is 2.5e+15\n",
"The sum of which s equal to 2.9e+15\n",
"The freq. corresponding to 2nd longest wavelength was found out to be 2.92622261239e+15 Hence Ritz combination principle is satisfied.\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6 Page 192"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"Rinfi=1.097*10**7; #known value \n",
"n1=3.0;n2=2.0; #first 2 given states\n",
"\n",
"#calculation\n",
"w=(n1**2*n2**2)/((n1**2-n2**2)*Rinfi);\n",
"\n",
"#result\n",
"print\"Wavelength of transition from n1=3 to n2=2 in nm is\",round(w*10**9,3);\n",
"\n",
"#partb\n",
"n1=4.0;n2=2.0; #second 2 given states \n",
"w=(n1**2*n2**2)/((n1**2-n2**2)*Rinfi);\n",
"\n",
"#result\n",
"print\"Wavelength of transition from n1=3 to n2=2 in nm is\",round(w*10**9,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Wavelength of trnasition from n1=3 to n2=2 in nm is 656.335\n",
"Wavelength of trnasition from n1=3 to n2=2 in nm is 486.174\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7 Page 194"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"n1=3.0;n2=2.0;Z=4.0;hc=1240.0;\n",
"delE=(-13.6)*(Z**2)*((1/(n1**2))-((1/n2**2)));\n",
"\n",
"#calculation\n",
"w=(hc)/delE; #for transition 1\n",
"\n",
"#result\n",
"print \"The wavelngth of radiation for transition(2->3) in nm is\", round(w,3);\n",
"\n",
"#for transition 2\n",
"n1=4.0;n2=2.0; # n values for transition 2\n",
"delE=(-13.6)*(Z**2)*((1/n1**2)-(1/n2**2));\n",
"w=(hc)/delE;\n",
"\n",
"#result\n",
"print \"The wavelngth of radiation emitted for transition(2->4) in nm is\", round(w,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelngth of radiation for transition(2->3) in nm is 41.029\n",
"The wavelngth of radiation emitted for transition(2->4) in nm is 30.392\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}