Assignment 1

Due on 30/1/03

Lennard-Jones Potential and Inert Gas atomic bonding

 Element epsilon (10 -16 erg) sigma (Angstrom) Experimental cohesive energy (eV/atom) Experimental cohesive energy (kJ/mol) Nearest neighbour distance (Angstrom) Melting point (K) Ne 50 2.74 0.02 1.88 3.13 24 Ar 167 3.40 0.08 7.74 3.76 84 Kr 225 3.65 0.116 11.2 4.01 117 Xe 320 3.98 0.17 16.0 4.35 161

(1) Use the above epsilon and sigma values in the expression for the Lennard-Jones potential

U(r) = 4 epsilon[ (sigma / r)12 -- (sigma / r)6 ]
to draw the U vs r curve [You can use MATLAB or equivalent software to plot the figures - using different symbols for the different elements if you are overlapping them in the same figure].

(2) Find the cohesive energy and the equilibrium seperation distance between the atoms of the different elements [If using MATLAB you can use the max and find functions to obtain it from the figures]. Compare the numbers you obtain with the experimental values given in the above table.

(3) Use the experimentally obtained values of cohesive energy to estimate the melting points of the different elements. Compare with the observed melting points given above.

Given:
Boltzmann constant, k = 1.38 x 10 -23 J/K = 8.617 x 10 -5 eV/K
Avogadro number, N0 = 6 x 10 23 /mol
1 eV = 1.602 x 10 -12 erg
MATLAB is available in imsc5, imsc6, imsc7