import math
#Given Data
h = 6.626*10**-34; # Planck's constant, Js
h_bar = h/(2*math.pi); # Reduced Planck's constant, Js
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
m = 9.1*10**-31; # Mass of an electron, kg
# For Na
n_Na = 2.65*10**28; # electronic concentration of Na, per metre cube
k_F = (3*math.pi**2*n_Na)**(1.0/3); # Fermi wave vector, per cm
E_F = h_bar**2*k_F**2/(2*m*e); # Fermi energy of Na, eV
print"The fermi energy of Na = ",round(E_F,4),"eV";
print"The band structure value of Na = ",0.263*13.6,"eV";
# For K
n_K = 1.4e+28; # electronic concentration of K, per metre cube
k_F = (3*math.pi**2*n_K)**(1.0/3); # Fermi wave vector, per cm
E_F = h_bar**2*k_F**2/(2*m*e); # Fermi energy of K, eV
print"The fermi energy of K = ",round(E_F,4),"eV";
print"The band structure value of K = ", 0.164*13.6,"eV";
print"The agreement between the free electron and band theoretical values are fairly good both for Na and K";
import math
#Given Data
n_Na = 2.65*10**22; # electronic concentration of Na, per cm cube
k_F = (3*math.pi**2*n_Na)**(1.0/3); # Fermi wave vector, per cm
print"The fermi momentum of Na =","{0:.3e}".format(k_F),"per cm";
import math
#Given Data
h = 6.626*10**-34; # Planck's constant, Js
h_bar = h/(2*math.pi); # Reduced Planck's constant, Js
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
m = 9.1*10**-31; # Mass of an electron, kg
V = 1.0*10**-6; # Volume of unit cube of material, metre cube
# For Mg
E_F = 7.13*e; # Fermi energy of Mg, J
s = 2*math.pi**2/(e*V)*(h_bar**2/(2*m))**(3.0/2)*(E_F)**(-1.0/2); # Energy separation between levels for Mg, eV
print"The energy separation between adjacent levels for Mg = ","{0:.3e}".format(s),"eV";
# For Cs
E_F = 1.58*e; # Fermi energy of Cs, J
s = 2*math.pi**2/(e*V)*(h_bar**2/(2*m))**(3.0/2)*(E_F)**(-1.0/2); # Energy separation between levels for Cs, eV
print"The energy separation between adjacent levels for Cs =","{0:.3e}".format(s),"eV";
import math
#Given Data
gamma_expt = 7.0*10**-4; # Experimental value of electronic specific heat, cal/mol/K-square
gamma_theory = 3.6*10**-4; # Theoretical value of electronic specific heat, cal/mol/K-square
L = (gamma_expt - gamma_theory)/gamma_theory;
print"The electron-phonon coupling constant of superconductor = ",round(L,2);
import math
#Given Data
N_Ef = 1.235; # Density of states at fermi energy, electrons/atom-eV
N = 6.023*10**23; # Avogadro's number
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Charge on an electron, C
gama = math.pi**2*k**2/3*(N_Ef*N/e); # Electronic specific heat coefficient, J/g-atom-kelvin square
print"The electronic specific heat coefficient of superconductor = ",round(gama*1000,4),"mJ/g-atom-kelvin square";
import math
#Given Data
gamma_expt = 4.84; # Experimental value of electronic specific heat of metal, mJ/g-atom/K-square
gamma_theory = 2.991; # Theoretical value of electronic specific heat of metal, mJ/g-atom/K-square
L = (gamma_expt-gamma_theory)/gamma_theory;
print"The electron-phonon coupling constant for metal = ",round(L,4);
import math
#Given data
mu_B = 9.24*10**-27; # Bohr's magneton, J/T
N_Ef = 0.826; # Density of states at fermi energy, electrons/atom-eV
N = 6.023*10**23; # Avogadro's number
e = 1.6*10**-19; # Energy equivalent of 1 eV, J
chi_Pauli = mu_B**2*N_Ef*N/e;
print"Pauli spin susceptibility of Mg = ","{0:.3e}".format( chi_Pauli*1000),"cgs units";