summaryrefslogtreecommitdiff
path: root/Modern_Physics/Chapter7.ipynb
diff options
context:
space:
mode:
Diffstat (limited to 'Modern_Physics/Chapter7.ipynb')
-rwxr-xr-xModern_Physics/Chapter7.ipynb231
1 files changed, 126 insertions, 105 deletions
diff --git a/Modern_Physics/Chapter7.ipynb b/Modern_Physics/Chapter7.ipynb
index 5f1ccec9..b8966938 100755
--- a/Modern_Physics/Chapter7.ipynb
+++ b/Modern_Physics/Chapter7.ipynb
@@ -1,7 +1,6 @@
{
"metadata": {
- "name": "",
- "signature": "sha256:75c249ea2e8c0a6e5f6f1e7aa12f02f35c3e7e62df28f6611e18b53d1b7e6dcd"
+ "name": "Chapter7"
},
"nbformat": 3,
"nbformat_minor": 0,
@@ -13,54 +12,34 @@
"level": 1,
"metadata": {},
"source": [
- "Chapter 7: Tunneling Phenomena"
+ "Chapter 7:The Hydrogen Atom in Wave Mechanics"
]
},
{
"cell_type": "heading",
- "level": 2,
+ "level": 1,
"metadata": {},
"source": [
- "Example 7.1, page no. 235"
+ "Example 7.2 Page 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "\n",
- "\n",
+ "#initiation of variable\n",
+ "from math import exp\n",
"import math\n",
+ "from scipy import integrate\n",
+ "# calculating radial probability P= (4/ao^3)*integral(r^2 * e^(-2r/ao)) between the limits 0 and ao for r\n",
"\n",
- "#Variable declaration\n",
- "h = 1.973 * 10**3 #planck's constant (eV.A'/c)\n",
- "me = 511 * 10**3 #mass of electron (eV/c^2)\n",
- "U = 10.0\n",
- "E = 7.0\n",
- "L = 50.00 #thickness of layer (A')\n",
- "\n",
- "#Calculation\n",
- "\n",
- "a = math.sqrt(2*me*(U-E))/h\n",
- "T=(1.0+(1.0/4.0)*(U**2/(E*(U-E)))*(math.sinh(a*L))**2)**-1\n",
- "\n",
- "#Result\n",
- "\n",
- "print \"The transmission coefficient for L=\",L,\"A' is\",round(T/10**-38,3),\"X 10^-38\"\n",
- "\n",
- "#(b)if the layer thickness is 1.00nm.\n",
- "\n",
- "#Variable Declaration\n",
- "\n",
- "L = 10 #thickness of layer (A')\n",
+ "#calculation\n",
+ "def integrand(x):\n",
+ " return ((x**2)*exp(-x))/2.0\n",
+ "Pr=integrate.quad(integrand,0,2,args=());#simplifying where as x=2*r/a0; hence the limits change between 0 to 2\n",
"\n",
- "#Calculation\n",
- "\n",
- "T=(1.0+(1.0/4.0)*(U**2/(E*(U-E)))*(math.sinh(a*L))**2)**-1\n",
- "\n",
- "#Result\n",
- "\n",
- "print \"The transmission coefficient for L=\",L,\"A' is\",round(T/10**-7,3),\"X 10^-7\""
+ "#result\n",
+ "print \"Hence the probability of finding the electron nearer to nucleus is\",round(Pr[0],3);\n"
],
"language": "python",
"metadata": {},
@@ -69,41 +48,44 @@
"output_type": "stream",
"stream": "stdout",
"text": [
- "The transmission coefficient for L= 50.0 A' is 0.963 X 10^-38\n",
- "The transmission coefficient for L= 10 A' is 0.657 X 10^-7\n"
+ "Hence the probability of finding the electron nearer to nucleus is 0.323\n"
]
}
],
- "prompt_number": 3
+ "prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
- "Example 7.2, page no. 236"
+ "Example 7.3 Page 213"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
+ "#initiation of variable\n",
+ "from math import exp\n",
+ "import math\n",
+ "from scipy import integrate\n",
+ "# employing the formula for probability distribution similarly as done in Exa-7.2 \n",
+ "#calculation\n",
+ "def integrand(x):\n",
+ " return (1.0/8)*((4.0*x**2)-(4.0*x**3)+(x**4))*exp(-x)\n",
+ "Pr1= integrate.quad(integrand,0,1,args=()) #x=r/ao; similrly limits between 0 and 1.\n",
"\n",
- "#Variable declaration\n",
- "\n",
- "e = 1.6 * 10 ** -19 #charge of electron (C)\n",
- "I = 1.00 * 10 ** -3 #electron current(A)\n",
- "T = 0.657 *10**-7 #Transmission coefficient\n",
- "\n",
- "#Calculation\n",
- "\n",
- "Ne = I / e\n",
- "Nadj = Ne * T\n",
- "Iadj = Nadj * e\n",
+ "#result\n",
+ "print\"The probability for l=0 electron is\",round(Pr1[0],5)\n",
"\n",
- "#Result\n",
+ "#part2\n",
+ "def integrand(x):\n",
+ " return (1.0/24)*(x**4)*(exp(-x))\n",
+ "Pr2=integrate.quad(integrand,0,1); #x=r/ao; similarly limits between 0 and 1.\n",
"\n",
- "print \"The number of electrons per second continuing on the adjacent wire is\",round(Nadj/10**8,2),\"X 10^8 and the transmitted current is\",round(Iadj/10**-12,1),\"pA.\""
+ "#result\n",
+ "print\"The probability for l=1 electron is\",round(Pr2[0],5)\n"
],
"language": "python",
"metadata": {},
@@ -112,46 +94,38 @@
"output_type": "stream",
"stream": "stdout",
"text": [
- "The number of electrons per second continuing on the adjacent wire is 4.11 X 10^8 and the transmitted current is 65.7 pA.\n"
+ "The probability for l=0 electron is 0.03432\n",
+ "The probability for l=1 electron is 0.00366\n"
]
}
],
- "prompt_number": 8
+ "prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
- "Example 7.5, page no. 241"
+ "Example 7.4 Page 215"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- "\n",
- "\n",
+ "#initiation of variable\n",
+ "from math import exp, sqrt\n",
"import math\n",
+ "from scipy import integrate\n",
+ "l=1.0; #given value of l\n",
"\n",
- "#Variable Declaration\n",
- "\n",
- "e = 1.6 * 10 **-19 #charge of electron(C)\n",
- "f = 1.0*10**30 #collision frequency (s^-1.cm^-2)\n",
- "Ec = 5.5 * 10 ** 10 \n",
- "V = 10 * 10 ** 3 #potential difference(V)\n",
- "d = 0.010 * 10**-3 #plate separation(m)\n",
- "\n",
- "#Calculation\n",
- "\n",
- "E = V /d\n",
- "Te = math.exp(-Ec/E)\n",
- "rate = f * Te\n",
- "I = e * rate\n",
+ "#calculation\n",
+ "am1=sqrt(l*(l+1)); #angular momentum==sqrt(l(l+1)) h\n",
+ "l=2.0 #given l\n",
+ "am2=sqrt(l*(l+1));\n",
"\n",
"#result\n",
- "\n",
- "print \"The tunneling current is\",round(I/10**-12,2),\"pA.\""
+ "print\"The angular momenta are found out to be\", round(am1,3),\" h and\",round(am2,3),\" h respectively for l=1 and l=2.\";\n"
],
"language": "python",
"metadata": {},
@@ -160,55 +134,102 @@
"output_type": "stream",
"stream": "stdout",
"text": [
- "The tunneling current is 0.21 pA.\n"
+ "The angular momenta are found out to be 1.414 h and 2.449 h respectively for l=1 and l=2.\n"
]
}
],
- "prompt_number": 12
+ "prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
- "Example 7.6, page no. 244"
+ "Example 7.5 Page 216"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
- " \n",
- "\n",
- "import math\n",
- "\n",
- "#Variable declaration\n",
- "\n",
- "Zth = 90 #atomic number of thorium\n",
- "Zdth = 88 #atomic number of thorium's daughter nucleus\n",
- "E = 4.05 #energy of ejected alphas(MeV)\n",
- "Zpo = 84 #atomic number of polonium\n",
- "Zdpo = 82 #atomic number of polonium's daughter nucleus\n",
- "Epo = 8.95 #energy of ejected alphas(MeV)\n",
- "R = 9.00 #nucleus size(fm)\n",
- "r0 = 7.25 #Bohr radius of alpha(fm)\n",
- "E0 = 0.0993 #(MeV)\n",
- "f = 10 ** 21 #collision frequency(Hz)\n",
- "\n",
- "\n",
- "#Calculation\n",
+ "#initiation of variable\n",
+ "from math import sqrt\n",
+ "print \"The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\";\n",
+ "print \"Length of the vector as found out previously is %.2f*h.\",round(sqrt(6),4);#angular momentum==sqrt(l(l+1)) h"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.\n",
+ "Length of the vector as found out previously is %.2f*h. 2.4495\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.6 Page 223"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#initiation of variable\n",
+ "uz=9.27*10**-24; t=1.4*10**3; x=3.5*10**-2; #various constants and given values\n",
+ "m=1.8*10**-25;v=750; # mass and velocity of the particle\n",
"\n",
- "Te = math.exp(-4*math.pi*Zdth*math.sqrt((E0/E))+ 8 * math.sqrt(Zdth*R/r0))\n",
- "rate = f * Te\n",
- "t = math.log(2)/rate\n",
- "Tep = math.exp(-4*math.pi*Zdpo*math.sqrt((E0/Epo))+ 8 * math.sqrt(Zdpo*R/r0))\n",
- "ratep = f * Tep\n",
- "tp = math.log(2)/ratep\n",
+ "#calculation\n",
+ "d=(uz*t*(x**2))/(m*(v**2)); #net separtion \n",
"\n",
+ "#result\n",
+ "print\"The distance of separation in mm is\",round(d*10**3,3);"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The distance of separation in mm is 0.157\n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 7.7 Page 227"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#initiation of variable\n",
+ "n1=1.0;n2=2.0;hc=1240.0; #hc=1240 eV.nm\n",
+ "E=(-13.6)*((1/n2**2)-(1/n1**2)); #Energy calculation\n",
"\n",
- "#Result\n",
+ "#calculation\n",
+ "w=hc/E; #wavelength\n",
+ "u=9.27*10**-24; B=2; #constants\n",
+ "delE= u*B/(1.6*10**-19); #change in energy\n",
+ "delw=((w**2/hc))*delE; #change in wavelength\n",
"\n",
- "print \"The half life of thorium is\",round(t/10**17,1),\"X 10^17 s and that of polonium is\",round(tp/10**-10,1),\"X 10^-10 s.\""
+ "#result\n",
+ "print\"The change in wavelength in nm. is\",round(delw,4);"
],
"language": "python",
"metadata": {},
@@ -217,11 +238,11 @@
"output_type": "stream",
"stream": "stdout",
"text": [
- "The half life of thorium is 5.4 X 10^17 s and that of polonium is 8.4 X 10^-10 s.\n"
+ "The change in wavelength in nm. is 0.0014\n"
]
}
],
- "prompt_number": 14
+ "prompt_number": 12
}
],
"metadata": {}
generated by cgit (git 2.34.1) at 2024-12-20 10:15:40 +0000