import math
#Given Data
rho = 7.9*10**3; # Density of iron, kg per cubic meter
A = 56*10**-3; # Atomic weight of iron, g/mol
N_A = 6.02*10**23; # Avogadro's number, atoms per mole
mu_B = 9.3*10**-24; # Bohr magneton; # Ampere meter square
n = rho*N_A/A; # Total number of atoms per unit cell, per cubic meter
M = 2.2*n*mu_B; # Spontaneous magnetization of iron, Ampere per meter
print"Spontaneous magnetization of iron =","{0:.3e}".format(M),"Ampere per meter";
import math
#Given Data
n = 3*10**28; # Spin density of electrons in a ferromagnetic material, per cubic meter
mu = 3*10**-23; # spin magnetic moment of a ferromagnetic material, Square Ampere
M_s = n*mu; # Saturation magnetization of a ferromagnetic material, Per Ampere
print"Saturation magnetization of a ferromagnetic material =","{0:.3e}".format(M_s),"ampere per meter";
import math
#Given Data
h_bar = 6.58*10**-16; # Planck's constant, eV.s
m = 0.511*10**6; # Mass of an electron, eV
e = 1.6*10**-12; # Energy equivalent of 1 eV, erg/eV
c = 3.0*10**10; # Speed of light, cm/s
N = 4.7*10**22; # Free electron gas concentration of Lithium, per cubic cm
mu_B = 9.27*10**-21; # Bohr magneton, Ampere cm-square
E_F = (h_bar*c)**2/(2*m)*(3*math.pi**2*N)**(2.0/3); # Fermi energy, eV
chi = 3*N*mu_B**2/(2*E_F*e); # Magnetic susceptibility of Lithium, cgs units
print"Magnetic susceptibility of Lithium =","{0:.3e}".format(chi),"cgs units";
import math
#Given Data
a_B = 0.53*10**-8; # Bohr radius, cm
N = 27*10**23; # Atomic density of He gas, per cubic cm
c = 3*10**10; # Speed of light, cm/sec
e = 1.6*10**-19; # Charge of an electron, Coulomb
m = 9.1*10**-28; # Mass of an electron, g
# As r_classic = e**2/(m*c**2), Classical radius of an electron
r_classic = 2.8*10**-13; # Classical radius of the electron, cm
chi = -2*N*r_classic/6*a_B**2; # Magnetic susceptibility of Helium, cgs units
print"Diamagnetic susceptibility of helium atom in ground state =","{0:.3e}".format(chi),"emu";
import math
#Given Data
chiA_He = 1.9*10**-6; # Atomic susceptibility of helium, cm cube per mole
chiA_Cu = 18*10**-6; # Atomic susceptibility of Copper, cm cube per mole
Q_sp = 1.77*10**7; # Specific charge of an electron, emu
Ne = 9650.0; # Charge of a gram ion, emu
Z_He = 2.0; # Atomic number of helium atom
Z_Cu = 29.0; # Atomic number of copper atom
R_He = math.sqrt(abs(-6*chiA_He/(Ne*Z_He*Q_sp))); # Magnetic susceptibility of helium atom, cgs units
R_Cu = math.sqrt(abs(-6*chiA_Cu/(Ne*Z_Cu*Q_sp))); # Magnetic susceptibility of copper atom, cgs units
print"Atomic radius of helium =","{0:.3e}".format(R_He),"cm";
print"Atomic radius of copper =","{0:.3e}".format(R_Cu),"cm";
import math
#Given Data
N = 6.039*10**22; # Atomic density of Neon gas, per cubic cm
# As r_classic = e**2/(m*c**2), Classical radius of an electron
r_classic = 2.8*10**-13; # Classical radius of the electron, cm
Z = 10.0; # Atomic number of helium atom
a0 = 0.53*10**-8; # Bohr's radius, cm
n1 = 2; n2 = 2; n3 = 6; # Occupation numbers for 1s, 2s and 2p states of Ne
r_sq_1s = 0.031; # Expectation value for 1s state
r_sq_2s = 0.905; # Expectation value for 2s state
r_sq_2p = 1.126; # Expectation value for 2p state
mean_r_sq = n1*r_sq_1s + n2*r_sq_2s + n3*r_sq_2p; # Mean square radius, cm-square
Chi_A = -1.0/6*N*Z*r_classic*mean_r_sq*a0**2; # Magnetic susceptibility of helium atom, cgs units
print"Atomic susceptibility of Ne atom =","{0:.3e}".format(Chi_A),"emu/mole";
import math
#Given Data
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
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
mu = e*h_cross/(2*m); # Bohr magneton, J/T
mu_H = mu/e; # Magnetic energy, eV
kT = 0.025; # Energy associated with two degrees of freedom, eV
E_ratio = mu_H/kT; # Exceptional terms in Langevin's function
print"The magnitude of mu*H/(k*T) =","{0:.3e}".format(E_ratio);
import math
#Given Data
mu = 5.78*10**-5; # Bohr magneton, eV/T
NE_F = 0.826; # Density of states at fermi level, electrons/atom-J
chi_Pauli = mu**2*NE_F/10**-4; # Pauli diamagnetism, cgs units
chi_Core = -4.2*10**-6; # Core diamagnetism, cgs units
chi_Landau = -1.0/3*chi_Pauli; # Landau diamagnetism, cgs units
chi_Total = chi_Core+ chi_Pauli+chi_Landau; # Paramagnetic susceptibility of Mg, cgs units
print"The paramagnetic susceptibility of Mg =","{0:.3e}".format(chi_Total),"cgs units";
import math
#Given Data
e = 1.6*10**-19; # Energy equivalent of 1 eV, J/eV
mu = 9.29*10**-24; # Bohr magneton, J/T
mu_0 = 1.26*10**-6; # Permeability of free space, Sq. tesla cubic meter per joule
E_F= 11.63*e; # Fermi energy, J
N = 6.02*10**28; # Atomic concentration, atoms per cubic meter
chi_Total = 2.2*10**-5; # Paramagnetic susceptibility of Mg, S.I. units
chi_Pauli = 3*N*mu**2*mu_0/(2*E_F); # Pauli diamagnetism, S.I. units
chi_dia = chi_Total - chi_Pauli; # Diamagnetic contribution to magnetic susceptibility
print"The Pauli spin susceptibility of Al =","{0:.3e}".format(chi_Pauli),"S.I. units";
print"The diamagnetic contribution to magnetic susceptibility of Al =","{0:.3e}".format(chi_dia),"S.I. units";
import math
#Given Data
a0 = 5.3; # Bohr radius, nm
rs_a0_ratio = 3.93; # Ratio of solid radius to the lattice parameter
chi_Pauli = 2.59/rs_a0_ratio; # Pauli's spin susceptibility, cgs units
print"The Pauli spin susceptibility for Na in terms of free electron gas parameter =",round(chi_Pauli,3);
import math
#Given Data
S = 2; # Spin quantum number
J = 0; # Total quantum number
L = 2; # Orbital quantum number
g = 2; # Lande splitting factor
print"The spectroscopic term value of Mn3+ ion =",2*S+1,"_D_",J;
# For J = L - S
J = L - S;
mu_N = g*math.sqrt(J*(J+1)); # Effective magneton number
print"The effective magneton number for J = L - S is",mu_N;
# For J = S, L = 0 so that
L = 0;
J = L+S;
mu_N = g*math.sqrt(J*(J+1)); # Effective magneton number
print"The effective magneton number for J = S is",round(mu_N,2),"\nIt is in agreement with the experimental value of 5.0.";
import math
#Given Data
mu = 9.27*10**-24; # Bohr's magneton, J/T
N_up = 5; # Number of electrons with spin up as per Hunds Rule
N_down = 1; # Number of electrons with spin down as per Hunds Rule
M = mu*(N_up-N_down); # Net magnetic moment associated with six electrons in the 3d shell, J/T
print"The magnetic moment of 3d electrons of Fe using Hunds rule =",M/mu,"Bohr magnetons";
import math
#Given Data
C = [[1,2,3,4],[5,6,7,8],[9,10,11,12]];
# Enter compound names
C[0][0] = 'LaCrO3';
C[1][0] = 'LaMnO3';
C[2][0] = 'LaCoO3';
# Enter Magnetic moments from Hunds rule
C[0][1] = 3.0;
C[1][1] = 4.0;
C[2][1] = 5.0;
# Enter Magnetic moments from Band theory
C[0][2] = 2.82;
C[1][2] = 3.74;
C[2][2] = 4.16;
# Enter Magnetic moments from the Experiment
C[0][3] = 2.80;
C[1][3] = 3.90;
C[2][3] = 4.60;
print"__________________________________________________";
print"Compound Magnetic moment per formula unit (in BM) ";
print" ________________________________________";
print" Hunds Rule Band Theory Experiment";
print"__________________________________________________";
for i in range (0,3) :
print"",C[i][0]," ",C[i][1]," ",C[i][2]," ",C[i][3]
print"__________________________________________________";
import math
#Given Data
C = [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]];
# Enter compound names
C[0][0] = 'LaTiO3';
C[1][0] = 'LaCrO3';
C[2][0] = 'LaFeO3';
C[3][0] = 'LaCoO3';
# Enter total energy difference w.r.t. ground state for Paramagnetics, mRyd
C[0][1] = 0.014;
C[1][1] = 158.3;
C[2][1] = 20.69;
C[3][1] = 0.000;
# Enter total energy difference w.r.t. ground state for Ferromagnetics, mRyd
C[0][2] = 0.034;
C[1][2] = 13.99;
C[2][2] = 0.006;
C[3][2] = 0.010;
# Enter total energy difference w.r.t. ground state for Antiferromagnetics, mRyd
C[0][3] = 0.000;
C[1][3] = 0.000;
C[2][3] = 0.000;
C[3][3] = 0.003;
print"______________________________________________________________";
print"Solid Total energy difference (mRyd) (w.r.t. ground state)";
print" ____________________________________________________";
print" Paramagnetic Ferromagnetic Antiferromagnetic ";
print"______________________________________________________________";
for i in range (0,4) :
print"",C[i][0]," ",C[i][1]," ",C[i][2]," ",C[i][3]
print"______________________________________________________________";
print"All the solids given above crystallize in the antiferromagnetic state except that of LaCoO3.";