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{
"metadata": {
"name": "",
"signature": "sha256:75c249ea2e8c0a6e5f6f1e7aa12f02f35c3e7e62df28f6611e18b53d1b7e6dcd"
},
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7: Tunneling Phenomena"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.1, page no. 235"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\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",
"\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\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"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"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.2, page no. 236"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\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",
"\n",
"#Result\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.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"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"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.5, page no. 241"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"import math\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",
"\n",
"#result\n",
"\n",
"print \"The tunneling current is\",round(I/10**-12,2),\"pA.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The tunneling current is 0.21 pA.\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7.6, page no. 244"
]
},
{
"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",
"\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",
"\n",
"\n",
"#Result\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.\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"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"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}
|
