import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Charge on an electron, C
n = 8.5*10**28; # Concentration of electron in Cu, per metre cube
rho = 1.7*10**-8; # Resistivity of Cu, ohm-m
t = m/(n*e**2*rho); # Collision time for an electron in monovalent Cu, s
print"The collision time for an electron in monovalent Cu =","{0:.3e}".format(t),"s";
import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Charge on an electron, C
n = 10**29; # Concentration of electron in material, per metre cube
rho = 27*10**-8; # Resistivity of the material, ohm-m
tau = m/(n*e**2*rho); # Collision time for an electron in the material, s
v_F = 1*10**8; # Velocity of free electron, cm/s
lamda = v_F*tau; # Mean free path of electron in the material, cm
print"The collision time for an electron in monovalent Cu =","{0:.3e}".format(tau),"s";
print"The mean free path of electron at 0K =","{0:.3e}".format(lamda),"cm";
import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Charge on an electron, C
r = 1.28*10**-10; # Atomic radius of cupper, m
a = 4*r/math.sqrt(2); # Lattice parameter of fcc structure of Cu, m
V = a**3; # Volume of unit cell of Cu, metre cube
n = 4/V; # Number of atoms per unit volume of Cu, per metre cube
tau = 2.7*10**-4; # Relaxation time for an electron in monovalent Cu, s
sigma = n*e**2*tau/m; # Electrical conductivity of Cu, mho per cm
print"The free electron density in monovalent Cu =","{0:.3e}".format(n),"per metre cube";
print"The electrical conductivity of monovalent Cu =","{0:.3e}".format(sigma),"mho per cm";
import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
h = 6.625*10**-34; # Planck's constant, Js
L = 10*10**-3; # Length of side of the cube, m
# For nth level
nx = 1; ny = 1; nz = 1; # Positive integers along three axis
En = h**2/(8*m*L**2)*(nx**2+ny**2+nz**2)/e; # Energy of nth level for electrons, eV
# For (n+1)th level
nx = 2; ny = 1; nz = 1; # Positive integers along three axis
En_plus_1 = h**2/(8*m*L**2)*(nx**2+ny**2+nz**2)/e; # Energy of (n+1)th level for electrons, eV
delta_E = En_plus_1 - En; # Energy difference between two levels for the free electrons
print"The energy difference between two levels for the free electrons =","{0:.3e}".format( delta_E),"eV";
import math
#Given Data
T = 300.0; # Room temperature of tungsten, K
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
E_F = 4.5*e; # Fermi energy of tungsten, J
E = E_F-0.1*E_F; # 10% energy below Fermi energy, J
f_T = 1.0/(1+math.exp((E-E_F)/(k*T))); # Probability of the electron in tungsten at room temperature at an nergy 10% below the Fermi energy
print"The probability of the electron at an energy 10 percent below the Fermi energy in tungsten at 300 K =",round(f_T,3);
E = 2*k*T+E_F; # For energy equal to 2kT + E_F
f_T = 1.0/(1+math.exp((E-E_F)/(k*T))); # Probability of the electron in tungsten at an energy 2kT above the Fermi energy
print"The probability of the electron at an energy 2kT above the Fermi energy =",round(f_T,4);
import math
#Given Data
h = 6.625*10**-34; # Planck's constant, Js
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
a = 5.34*10**-10; # Lattice constant of monovalent bcc lattice, m
V = a**3; # Volume of bcc unit cell, metre cube
n = 2.0/V; # Number of atoms per metre cube
E_F = h_cross**2.0/(2*m*e)*(3*math.pi**2*n)**(2.0/3); # Fermi energy of monovalent bcc solid, eV
print"The Fermi energy of a monovalent bcc solid =",round(E_F,4),"eV";
import math
#Given Data
h = 6.625*10**-34; # Planck's constant, Js
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
m = 9.11*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
V = 1*10**-5; # Volume of cubical box, metre cube
E_F = 5*e; # Fermi energy, J
D_EF = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*E_F**(1.0/2)*e; # Density of states at Fermi energy, states/eV
print"The density of states at Fermi energy =","{0:.3e}".format( D_EF),"states/eV";
import math
#Given Data
h = 6.626*10**-34; # Planck's constant, Js
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
V = 1*10**-6; # Volume of cubical box, metre cube
E_F = 7.13*e; # Fermi energy for Mg, J
D_EF = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*E_F**(1.0/2); # Density of states at Fermi energy for Cs, states/eV
E_Mg = 1.0/D_EF; # The energy separation between adjacent energy levels of Mg, J
print"The energy separation between adjacent energy levels of Mg =","{0:.3e}".format(E_Mg/e),"eV";
E_F = 1.58*e; # Fermi energy for Cs, J
D_EF = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*E_F**(1.0/2); # Density of states at Fermi energy for Mg, states/eV
E_Mg = 1.0/D_EF; # The energy separation between adjacent energy levels of Cs, J
print"The energy separation between adjacent energy levels of Cs =","{0:.3e}".format(E_Mg/e),"eV";
import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
E_F = 3.2*e; # Fermi energy of sodium, J
P_F = math.sqrt(E_F*2*m); # Fermi momentum of sodium, kg-m/s
print"The Fermi momentum of sodium =","{0:.3e}".format(P_F),"kg-m/sec";
import math
#Given Data
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
T = 500.0; # Rise in temperature of Al, K
EF_0 = 11.63; # Fermi energy of Al, eV
EF_T = EF_0*(1-math.pi**2.0/12*(k*T/EF_0)**2); # Change in Fermi energy of Al with temperature, eV
print"The change in Fermi energy of Al with tempertaure rise of 500 degree celsius =",round(EF_T,3),"eV";
import math
#Given Data
m = 9.18*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Charge on an electron, C
lamda = 1.0*10**-9; # Mean free path of electron in metal, m
v = 1.11*10**5; # Average velocity of the electron in metal, m/s
# For Lead
n = 13.2*10**28; # Electronic concentration of Pb, per metre cube
sigma = n*e**2*lamda/(m*v); # Electrical conductivity of lead, mho per metre
print"The electrical conductivity of lead =","{0:.3e}".format(sigma),"mho per metre";
# For Silver
n = 5.85*10**28; # Electronic concentration of Ag, per metre cube
sigma = n*e**2*lamda/(m*v); # Electrical conductivity of Ag, mho per metre
print"The electrical conductivity of silver =","{0:.3e}".format(sigma),"mho per metre";
import math
#Given Data
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Charge on an electron, C
L = math.pi**2.0/3*(k/e)**2; # Lorentz number, watt-ohm/degree-square
print"The Lorentz number =","{0:.3e}".format(L),"watt-ohm/degree-square";
import math
#Given Data
A =[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]; # Declare a 4X4 cell
A[0][0] = 'Mg';
A[0][1] = 2.54*10**-5;
A[0][2] = 1.5;
A[0][3] = 2.32*10**2;
A[1][0] = 'Cu';
A[1][1] = 6.45*10**-5;
A[1][2] = 3.85;
A[1][3] = 2.30*10**2;
A[2][0] = 'Al';
A[2][1] = 4.0*10**-5;
A[2][2] = 2.38;
A[2][3] = 2.57*10**2;
A[3][0] = 'Pt';
A[3][1] = 1.02*10**-5;
A[3][2] = 0.69;
A[3][3] = 2.56*10**2;
T1 = 273; # First temperature, K
T2 = 373; # Second temperature, K
print"_________________________________________________________________";
print"Metal sigma x 10**-05 K(W/cm-K) Lorentz number ";
print" (mho per cm) (watt-ohm/deg-square)x10**-2";
print"_________________________________________________________________";
for i in range (0,4) :
L1 = A[i][2]/(A[i][1]*T1);
L2 = A[i][3];
print"",A[i][0]," ",A[i][1]/10**-5," ",A[i][2]," ",L2/10**2," ",L2/10**2;
print"_________________________________________________________________";
import math
#Given Data
A = [[1,2],[3,4]]; # Declare a 2X3 cell
A[0][0] = 1.6*10**8; # Electrcal conductivity of Au at 100 K, mho per metre
A[0][1] = 2.0*10**-8; # Lorentz number of Au at 100 K, volt/K-square
A[1][0] = 5.0*10**8; # Electrcal conductivity of Au at 273 K, mho per metre
A[1][1] = 2.4*10**-8; # Lorentz number of Au at 273 K, volt/K-square
T1 = 100; # First temperature, K
T2 = 273; # Second temperature, K
print"___________________________________________________________________________";
print" T = 100 K T = 273 K ";
print"_________________________________ ___________________________________";
print"Electrical conductivity) L Electrical conductivity) L ";
print" mho per metre V/K-square mho per metre V/K-square";
print"___________________________________________________________________________";
K1 = A[0][0]*T1*A[0][1];
K2 = A[1][0]*T2*A[1][1];
print"{0:.3e}".format(A[0][0])," ","{0:.3e}".format(A[0][1])," ","{0:.3e}".format(A[1][0])," ","{0:.3e}".format(A[1][1])
print"K =",K1,"W/cm-K K =",K2,"W/cm-K";
print"___________________________________________________________________________";
import math
#Given Data
e = 1.6*10**-19; # Electronic charge, C
a = 0.428*10**-9; # Lattice constant of Na, m
V = a**3; # Volume of unit cell, metre cube
N = 2; # No. of atoms per unit cell of Na
n = N/V; # No. of electrons per metre cube, per metre cube
R_H = -1.0/(n*e); # Hall coeffcient of Na, metre cube per coulomb
print"The Hall coefficient of sodium =","{0:.3e}".format(R_H),"metre cube per coulomb";
import math
#Given Data
e = 1.6*10**-19; # Electronic charge, C
n = 24.2*10**28; # No. of electrons per metre cube, per metre cube
R_H = -1.0/(n*e); # Hall coeffcient of Be, metre cube per coulomb
print"The Hall coefficient of beryllium =","{0:.3e}".format(R_H),"metre cube per coulomb";
import math
#Given Data
e = 1.6*10**-19; # Electronic charge, C
R_H = -8.4*10**-11; # Hall coeffcient of Ag, metre cube per coulomb
n = -3*math.pi/(8*R_H*e); # Electronic concentration of Ag, per metre cube
print"The electronic concentration of Ag =","{0:.3e}".format(n),"per metre cube";
import math
#Given Data
# We have from Mattheissen rule, rho = rho_0 + alpha*T1
T1 = 300.0; # Initial temperature, K
T2 = 1000.0; # Final temperature, K
rho = 1*10**-6; # Resistivity of the metal, ohm-m
delta_rho = 0.07*rho; # Increase in resistivity of metal, ohm-m
alpha = delta_rho/(T2-T1); # A constant, ohm-m/K
rho_0 = rho - alpha*T1; # Resistivity at room temperature, ohm-m
print"The resistivity at room temperature =","{0:.3e}".format(rho),"ohm-m";
import math
#Given Data
# We have from Mattheissen rule, rho = rho_0 + alpha*T1
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
rho_40 = 0.2; # Resistivity of Ge at 40 degree celsius, ohm-m
E_g = 0.7; # Bandgap for Ge, eV
T1 = 20+273; # Second temperature, K
T2 = 40 + 273; # First temperature, K
rho_20 = rho_40*math.exp(E_g*e/(2*k)*(1.0/T1-1.0/T2)); # Resistivity of Ge at 20 degree celsius, ohm-m
print"The resistivity of Ge at 20 degree celsius =",round(rho_20,1),"ohm-m";
import math
#Given Data
rs_a0_ratio = 3.25; # Ratio of solid radius to the lattice parameter
E_F = 50.1*(rs_a0_ratio)**(-2); # Fermi level energy of Li, eV
T_F = 58.2e+04*(rs_a0_ratio)**(-2); # Fermi level temperature of Li, K
V_F = 4.20e+08*(rs_a0_ratio)**(-1); # Fermi level velocity of electron in Li, cm/sec
K_F = 3.63e+08*(rs_a0_ratio)**(-1);
print"E_F =",round(E_F,2),"eV";
print"T_F =","{0:.3e}".format(T_F),"K";
print"V_F =","{0:.3e}".format(V_F),"cm/sec";
print"K_F =","{0:.3e}".format(K_F),"per cm";
import math
#Given Data
n = 6.04*10**22; # Concentration of electrons in yittrium, per metre cube
r_s = (3/(4*math.pi*n))**(1.0/3)/10**-8; # Radius of the solid, angstrom
a0 = 0.529; # Lattice parameter of yittrium, angstrom
rs_a0_ratio = r_s/a0; # Solid radius to lattice parameter ratio
E_F = 50.1*(rs_a0_ratio)**(-2); # Fermi level energy of Y, eV
print"The Fermi energy of yittrium =",round(E_F,4),"eV";
Ryd = 13.6; # Rydberg energy constant, eV
E_bs = 0.396*Ryd; # Band structure energy value of Y, eV
print"The band structure value of E_F =",round(E_bs,3),"eV is in close agreement with the calculated value of",round(E_F,4),"eV";
import math
#Given Data
rs_a0_ratio = 2.07; # Solid radius to lattice parameter ratio for Al
E_F = 50.1*(rs_a0_ratio)**(-2); # Fermi level energy of Y, eV
# According to Jellium model, h_cross*omega_P = E = 47.1 eV *(rs_a0_ratio)**(-3/2)
E = 47.1*(rs_a0_ratio)**(-3.0/2); # Plasmon energy of Al, eV
print"The plasmon energy of Al =",round(E,4),"eV";
print"The experimental value is 15 eV";
import math
#Given Data
E_F = 1; # For simplicity assume Fermi energy to be unity, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
dE = 0.1; # Exces energy above Fermi level, eV
T = 300; # Room temperature, K
E = E_F + dE; # Energy of the level above Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV above E_F
print"At 300 K:";
print"=========";
print"The occupation probability of electron at",round(dE,3),"eV above Fermi energy =",round(f_E,3);
E = E_F - dE; # Energy of the level below Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV below E_F
print"The occupation probability of electron at",round(dE,3),"below Fermi energy =",round(f_E,3);
T = 1000; # New temperature, K
print"At 1000 K:";
print"=========";
E = E_F + dE; # Energy of the level above Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV above E_F
print"The occupation probability of electron at",round(dE,3),"eV above Fermi energy =",round(f_E,3);
E = E_F - dE; # Energy of the level below Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV below E_F
print"The occupation probability of electron at",round(dE,3),"eV below Fermi energy =",round(f_E,3);
import math
#Given Data
f_E = 0.01; # Occupation probability of electron
E_F = 1; # For simplicity assume Fermi energy to be unity, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
dE = 0.5; # Exces energy above Fermi level, eV
E = E_F + dE; # Energy of the level above Fermi level, eV
# We have, f_E = 1/(exp((E-E_F)*e/(k*T))+1), solving for T
T = (E-E_F)*e/k*1.0/math.log(1.0/f_E-1); # Temperature at which the electron will have energy 0.1 eV above the Fermi energy, K
print"The temperature at which the electron will have energy",round(dE,3),"eV above the Fermi energy =",round(T,3),"K";
import math
#Given Data
E_F = 10; # Fermi energy of electron in metal, eV
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
m = 9.1*10**-31; # Mass of an electron, kg
E_av = 3.0/5*E_F; # Average energy of free electron in metal at 0 K, eV
V_F = math.sqrt(2*E_av*e/m); # Speed of free electron in metal at 0 K, eV
print"The average energy of free electron in metal at 0 K =",round(E_av,3),"eV";
print"The speed of free electron in metal at 0 K =","{0:.3e}".format(V_F),"m/s";
import math
#Given Data
f_E = 0.1; # Occupation probability of electron
E_F = 5.5; # Fermi energy of Cu, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
dE = 0.05*E_F; # Exces energy above Fermi level, eV
E = E_F + dE; # Energy of the level above Fermi level, eV
# We have, f_E = 1/(exp((E-E_F)*e/(k*T))+1), solving for T
T = (E-E_F)*e/k*1.0/math.log(1.0/f_E-1); # Temperature at which the electron will have energy 0.1 eV above the Fermi energy, K
print"The temperature at which the electron will have energy",round(dE/E_F*100,3),"percent above the Fermi energy",round(T,3),"K";
#(The answer given in the textbook is wrong)
import math
#Given Data
T_F = 24600; # Fermi temperature of potassium, K
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
m = 9.1*10**-31; # Mass of an electron, kg
E_F = k*T_F; # Fermi energy of potassium, eV
v_F = math.sqrt(2*k*T_F/m); # Fermi velocity of potassium, m/s
print"The Fermi velocity of potassium =","{0:.3e}".format(v_F),"m/s";
import math
#Given Data
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
E_F = 7.0; # Fermi energy of Cu, eV
f_E = 0.9; # Occupation probability of Cu
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
T = 1000; # Given temperature, K
# We have, f_E = 1/(exp((E-E_F)*e/(k*T))+1), solving for E
E = k*T*math.log(1.0/f_E-1) + E_F*e; # Energy level of Cu for 10% occupation probability at 1000 K, J
print"The energy level of Cu for 10 percent occupation probability at 1000 K =",round(E/e,3),"eV";
import math
#Given Data
m = 9.1*10**-31; # Mass of an electron, kg
e = 1.6*10**-19; # Electronic charge, C
h = 6.626*10**-34; # Planck's constant, Js
E_F = 1.55; # Fermi energy of Cu, eV
n = (math.pi/3)*(8*m/h**2)**(3.0/2)*(E_F*e)**(3.0/2); # Electronic concentration in cesium, electrons/cc
print"The electronic concentration in cesium =","{0:.3e}".format(n),"electrons/cc";
import math
#Given Data
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
E_F = 7; # Fermi energy, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
T_F = E_F*e/k; # Fermi temperature, K
print"The Fermi temperature corresponding to Fermi energy =","{0:.3e}".format(T_F),"K";
import math
#Given Data
m = 9.1*10**-31; # Mass of the electron, kg
h = 6.626*10**-34; # Planck's constant, Js
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
s = 0.01; # Side of the box, m
E = 2; # Energy range of the electron in the box, eV
V = s**3; # Volume of the box, metre cube
I = I = 2*E**(3.0/2)/3; # Definite integral over E : I = 2*E**(3/2)/3
D_E = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*I*e**(3.0/2); # Density of states for the electron in a cubical box, states
print"The density of states for the electron in a cubical box =","{0:.3e}".format(D_E),"states";
import math
#Given Data
E_F = 1; # For simplicity assume Fermi energy to be unity, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
dE = 0.5; # Exces energy above Fermi level, eV
T = 300; # Room temperature, K
E = E_F + dE; # Energy of the level above Fermi level, eV
f_E = 1./(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV above E_F
print"At 300 K:";
print"=========";
print"The occupation probability of electron at",dE,"eV above Fermi energy =","{0:.3e}".format(f_E);
E = E_F - dE; # Energy of the level below Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV below E_F
print"The occupation probability of electron at",dE,"eV above Fermi energy =","{0:.3e}".format(f_E);
import math
#Given Data
E_F = 1; # For simplicity assume Fermi energy to be unity, eV
k = 1.38*10**-23; # Boltzmann constant, J/mol/K
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
dE = 0.2; # Exces energy above Fermi level, eV
T = 0+273; # Room temperature, K
E = E_F + dE; # Energy of the level above Fermi level, eV
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV above E_F
print"At 273 K:";
print"=========";
print"The occupation probability of electron at",dE,"eV above Fermi energy =","{0:.3e}".format(f_E);
T = 100+273; # Given temperature of 100 degree celsius, K
f_E = 1.0/(math.exp((E-E_F)*e/(k*T))+1); # Occupation probability of the electron at 0.1 eV below E_F
print"At 373 K:";
print"=========";
print"The occupation probability of electron at",dE,"eV above Fermi energy =","{0:.3e}".format(f_E);
import math
#Given Data
m = 9.1*10**-31; # Mass of the electron, kg
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
r = 1.28*10**-10; # Atomic radius of Cu, m
a = 4*r/math.sqrt(2); # Lattice constant of Cu, m
tau = 2.7*10**-14; # Relaxation time for the electron in Cu, s
V = a**3; # Volume of the cell, metre cube
n = 4.0/V; # Concentration of free electrons in monovalent copper,
sigma = n*e**2*tau/m; # Electrical conductivity of monovalent copper, mho per m
print"The electrical conductivity of monovalent copper =","{0:.3e}".format( sigma/100),"mho per cm";
import math
#Given Data
n = 18.1*10**22; # Number of electrons per unit volume, per cm cube
N = n/2; # Pauli's principle for number of energy levels, per cm cube
E_F = 11.58; # Fermi energy of Al, eV
E = E_F/N; # Interelectronic energy separation between bands of Al, eV
print"The interelectronic energy separation between bands of Al =","{0:.3e}".format(E),"eV";
import math
#Given Data
m = 9.1*10**-31; # Mass of the electron, kg
h = 6.626*10**-34; # Planck's constant, Js
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
E_F = 7; # Fermi energy of Cu, eV
V = 10**-6; # Volume of the cubic metal, metre cube
D_EF = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*(E_F)**(1.0/2)*e**(3.0/2); # Density of states in Cu contained in cubic metal, states/eV
print"The density of states in Cu contained in cubic metal =","{0:.3e}".format(D_EF),"states/eV";
import math
#Given Data
m = 9.1*10**-31; # Mass of the electron, kg
h = 6.626*10**-34; # Planck's constant, Js
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
h_cross = h/(2*math.pi); # Reduced Planck's constant, Js
E_F = 7; # Fermi energy of Cu, eV
V = 10**-6; # Volume of the cubic metal, metre cube
D_EF = V/(2*math.pi**2)*(2*m/h_cross**2)**(3.0/2)*(E_F)**(1.0/2)*e**(3.0/2); # Density of states in Cu contained in cubic metal, states/eV
d = 1.0/(D_EF); # Electronic energy level spacing between successive levels of Cu, eV
print"The electronic energy level spacing between successive levels of Cu =","{0:.3e}".format(d),"eV";
import math
#Given Data
A = [[1,2],[3,4],[5,6],[7,8]]; # Declare a 4X2 matrix
A[0][0] = 'Li';
A[0][1] = -0.4039; # Energy of outermost atomic orbital of Li, Rydberg unit
A[1][0] = 'Na'; #
A[1][1] = -0.3777; # Energy of outermost atomic orbital of Na, Rydberg unit
A[2][0] = 'F'; #
A[2][1] = -1.2502; # Energy of outermost atomic orbital of F, Rydberg unit
A[3][0] = 'Cl'; #
A[3][1] = -0.9067; # Energy of outermost atomic orbital of Cl, Rydberg unit
cf = 13.6; # Conversion factor for Rydberg to eV
print"________________________________________";
print" Atom Energy gap";
print"",A[1][0],A[3][0]," ",(A[1][1]-A[3][1])*cf,"eV";
print"",A[1][0],A[2][0]," ",(A[1][1]-A[2][1])*cf,"eV";
print"",A[0][0],A[2][0]," ",(A[0][1]-A[2][1])*cf,"eV";
print"________________________________________";
import math
#Given Data
# For Cu
rs_a0_ratio = 2.67; # Ratio of solid radius to the lattice parameter
E_F = 50.1*(rs_a0_ratio)**(-2); # Fermi level energy of Cu, eV
T_F = 58.2*10**4*(rs_a0_ratio)**(-2); # Fermi level temperature of Cu, K
V_F = 4.20*10**8*(rs_a0_ratio)**(-1); # Fermi level velocity of electron in Cu, cm/sec
K_F = 3.63*10**8*(rs_a0_ratio)**(-1);
print"For Cu :";
print"========";
print"E_F =",round(E_F,3),"eV";
print"T_F =","{0:.3e}".format(T_F),"K";
print"V_F =","{0:.3e}".format(V_F),"cm/sec";
print"K_F =","{0:.3e}".format(K_F),"per cm";
rs_a0_ratio = 3.07; # Ratio of solid radius to the lattice parameter
E_F = 50.1*(rs_a0_ratio)**(-2); # Fermi level energy of Nb, eV
T_F = 58.2*10**4*(rs_a0_ratio)**(-2); # Fermi level temperature of Nb, K
V_F = 4.20*10**8*(rs_a0_ratio)**(-1); # Fermi level velocity of electron in Nb, cm/sec
K_F = 3.63*10**8*(rs_a0_ratio)**(-1);
print"For Nb :";
print"========";
print"E_F =",round(E_F,3),"eV";
print"T_F =","{0:.3e}".format(T_F),"K";
print"V_F =","{0:.3e}".format(V_F),"cm/sec";
print"K_F =","{0:.3e}".format(K_F),"per cm";