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// Scilab Code Ex1.31: : Page-1.44 (2009)
clc; clear;
h = 6.6e-034; // Planck's constant, Js
m = 9.1e-031; // Electronic mass, kg
e = 1.6e-019; // Energy equivalent of 1 eV, J/eV
l = 2e-002; // Length of the side of the cube, m
E_F = 9*e; // Fermi energy, J
// As E_F = h^2/(8*m*l^2)*(nx^2 + ny^2 + nz^2) and nx = ny = nz for a cube, solving for nx
nx = sqrt(E_F*(8*m*l^2)/(3*h^2)); // Value of integer for a cube
E = h^2/(8*m*l^2)*3*nx^2; // Fermi energy, J
E1 = h^2/(8*m*l^2)*((nx-1)^2 + nx^2 + nx^2); // Energy of the level just below the fermi level, J
delta_E = E - E1; // Difference in the energy between the neighbouring levels of Na at the highest state, J
printf("\nThe energy difference between the neighbouring levels of Na at the highest state = %4.2e eV", delta_E/e);
// Result
// The energy difference between the neighbouring levels of Na at the highest state = 1.06e-07 eV
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