{
"metadata": {
"name": "",
"signature": "sha256:7388a73b9b3de996a0d87179cb12d51f5ad7f3cb764b14aa844019e8d2cdb4ea"
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"7: Superconductivity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.1, Page number 152"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Tc=3.722; #critical temperature(K)\n",
"T=2; #temperature(K)\n",
"Bc_0=0.0305; #critical field(T)\n",
"\n",
"#Calculation\n",
"Bc_T=Bc_0*(1-(T/Tc)**2); #critical field at 2K(T)\n",
"Bc_T = math.ceil(Bc_T*10**4)/10**4; #rounding off the value of Bc_T to 4 decimals\n",
"\n",
"#Result\n",
"print \"The critical field at 2K is\",Bc_T, \"T\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical field at 2K is 0.0217 T\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.2, Page number 152"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"V = 1; #DC voltage applied across the Josephson junction(micro-volt)\n",
"e = 1.6*10**-19; #Charge on an electron(C)\n",
"h = 6.626*10**-34; #Planck's constant(Js)\n",
"\n",
"#Calculation\n",
"V = V*10**-6; #DC voltage applied across the Josephson junction(V)\n",
"f = 2*e*V/h; #Frequency of Josephson current(Hz)\n",
"f = f*10**-6; #Frequency of Josephson current(MHz)\n",
"f = math.ceil(f*10**2)/10**2; #rounding off the value of f to 2 decimals\n",
"\n",
"#Result\n",
"print \"The frequency of Josephson current is\",f, \"MHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The frequency of Josephson current is 482.95 MHz\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.3, Page number 152"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"`\n",
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"T_c = 0.517; #Critical temperature for cadmium(K)\n",
"k = 1.38*10**-23; #Boltzmann constant(J/K)\n",
"e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
"\n",
"#Calculation\n",
"E_g = 3.5*k*T_c/e; #Superconducting energy gap at absolute zero(eV)\n",
"E_g = E_g*10**4;\n",
"E_g = math.ceil(E_g*10**3)/10**3; #rounding off the value of E_g to 3 decimals\n",
"\n",
"#Result\n",
"print \"The superconducting energy gap for Cd at absolute zero is\",E_g,\"*10**-4 eV\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The superconducting energy gap for Cd at absolute zero is 1.561 *10**-4 eV\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.4, Page number 152"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n",
"c = 3*10**8; #Speed of light in free space(m/s)\n",
"h = 6.626*10**-34; #Planck's constant(Js)\n",
"E_g = 1.5*10**-4; #Superconducting energy gap for a material(eV)\n",
"\n",
"#Calculation\n",
"#As E_g = h*new = h*c/lamda, solving for lambda\n",
"lamda = h*c/(E_g*e); #Wavelength of photon to break up a Cooper-pair(m)\n",
"lamda = lamda*10**3;\n",
"lamda = math.ceil(lamda*10**3)/10**3; #rounding off the value of lamda to 3 decimals\n",
"\n",
"#Result\n",
"print \"The wavelength of photon to break up a Cooper-pair is\",lamda,\"*10**-3 m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The wavelength of photon to break up a Cooper-pair is 8.283 *10**-3 m\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.5, Page number 153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"lambda_0 = 37; #Penetration depth of lead at 0 kelvin(nm)\n",
"T_c = 7.193; #Critical temperature of superconducting transition for lead(kelvin)\n",
"T = 5.2; #Temperature at which penetration depth for lead becomes lambda_T(kelvin) \n",
"\n",
"#Calculation\n",
"lambda_T = lambda_0*(1-(T/T_c)**4)**(-1/2); #Penetration depth of lead at 5.2 kelvin(nm)\n",
"lambda_T = math.ceil(lambda_T*10)/10; #rounding off the value of lamda_T to 1 decimal\n",
"\n",
"#Result\n",
"print \"The penetration depth of lead is\",lambda_T, \"nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The penetration depth of lead is 43.4 nm\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example number 7.6, Page number 153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#importing modules\n",
"from __future__ import division\n",
"import math\n",
"\n",
"#Variable declaration\n",
"M1 = 199; #Mass of an isotope of mercury(amu)\n",
"T_C1 = 4.185; #Transition temperature of the isoptope of Hg(K)\n",
"T_C2 = 4.153; #Transition temperature of another isoptope of Hg(K)\n",
"alpha = 0.5; #Isotope coefficient\n",
"\n",
"#Calculation\n",
"M2 = M1*(T_C1/T_C2)**(1/alpha); #Mass of another isotope of mercury(amu)\n",
"M2 = math.ceil(M2*100)/100; #rounding off the value of M2 to 2 decimals\n",
"\n",
"#Result\n",
"print \"The mass of another isotope of mercury is\",M2, \"amu\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mass of another isotope of mercury is 202.08 amu\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}