7: Superconductivity

Example number 7.1, Page number 152

In [1]:
#importing modules
from __future__ import division
import math

#Variable declaration
Tc=3.722;      #critical temperature(K)
T=2;          #temperature(K)
Bc_0=0.0305;     #critical field(T)

#Calculation
Bc_T=Bc_0*(1-(T/Tc)**2);     #critical field at 2K(T)
Bc_T = math.ceil(Bc_T*10**4)/10**4;     #rounding off the value of Bc_T to 4 decimals

#Result
print "The critical field at 2K is",Bc_T, "T"

The critical field at 2K is 0.0217 T

Example number 7.2, Page number 152

In [2]:
#importing modules
from __future__ import division
import math

#Variable declaration
V = 1;     #DC voltage applied across the Josephson junction(micro-volt)
e = 1.6*10**-19;    #Charge on an electron(C)
h = 6.626*10**-34;    #Planck's constant(Js)

#Calculation
V = V*10**-6;     #DC voltage applied across the Josephson junction(V)
f = 2*e*V/h;      #Frequency of Josephson current(Hz)
f = f*10**-6;      #Frequency of Josephson current(MHz)
f = math.ceil(f*10**2)/10**2;     #rounding off the value of f to 2 decimals

#Result
print "The frequency of Josephson current is",f, "MHz"

The frequency of Josephson current is 482.95 MHz

Example number 7.3, Page number 152

In [8]:
`

#importing modules
from __future__ import division
import math

#Variable declaration
T_c = 0.517;    #Critical temperature for cadmium(K)
k = 1.38*10**-23;    #Boltzmann constant(J/K)
e = 1.6*10**-19;     #Energy equivalent of 1 eV(J/eV)

#Calculation
E_g = 3.5*k*T_c/e;    #Superconducting energy gap at absolute zero(eV)
E_g = E_g*10**4;
E_g = math.ceil(E_g*10**3)/10**3;     #rounding off the value of E_g to 3 decimals

#Result
print "The superconducting energy gap for Cd at absolute zero is",E_g,"*10**-4 eV"

The superconducting energy gap for Cd at absolute zero is 1.561 *10**-4 eV

Example number 7.4, Page number 152

In [12]:
#importing modules
from __future__ import division
import math

#Variable declaration
e = 1.6*10**-19;    #Energy equivalent of 1 eV(J/eV)
c = 3*10**8;     #Speed of light in free space(m/s)
h = 6.626*10**-34;    #Planck's constant(Js)
E_g = 1.5*10**-4;     #Superconducting energy gap for a material(eV)

#Calculation
#As E_g = h*new = h*c/lamda, solving for lambda
lamda = h*c/(E_g*e);    #Wavelength of photon to break up a Cooper-pair(m)
lamda = lamda*10**3;
lamda = math.ceil(lamda*10**3)/10**3;     #rounding off the value of lamda to 3 decimals

#Result
print "The wavelength of photon to break up a Cooper-pair is",lamda,"*10**-3 m"

The wavelength of photon to break up a Cooper-pair is 8.283 *10**-3 m

Example number 7.5, Page number 153

In [13]:
#importing modules
from __future__ import division
import math

#Variable declaration
lambda_0 = 37;     #Penetration depth of lead at 0 kelvin(nm)
T_c = 7.193;      #Critical temperature of superconducting transition for lead(kelvin)
T = 5.2;        #Temperature at which penetration depth for lead becomes lambda_T(kelvin) 

#Calculation
lambda_T = lambda_0*(1-(T/T_c)**4)**(-1/2);     #Penetration depth of lead at 5.2 kelvin(nm)
lambda_T = math.ceil(lambda_T*10)/10;     #rounding off the value of lamda_T to 1 decimal

#Result
print "The penetration depth of lead is",lambda_T, "nm"

The penetration depth of lead is 43.4 nm

Example number 7.6, Page number 153

In [16]:
#importing modules
from __future__ import division
import math

#Variable declaration
M1 = 199;    #Mass of an isotope of mercury(amu)
T_C1 = 4.185;    #Transition temperature of the isoptope of Hg(K)
T_C2 = 4.153;    #Transition temperature of another isoptope of Hg(K)
alpha = 0.5;     #Isotope coefficient

#Calculation
M2 = M1*(T_C1/T_C2)**(1/alpha);    #Mass of another isotope of mercury(amu)
M2 = math.ceil(M2*100)/100;     #rounding off the value of M2 to 2 decimals

#Result
print "The mass of another isotope of mercury is",M2, "amu"

The mass of another isotope of mercury is 202.08 amu
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