compute the theoretical density of copper with the above information Problem 3:

Question

compute the theoretical density of copper with the above information

Problem 3: The bonding energy between two ions is given as the sum of repulsive (R) and attractive (A) energies as follows: 80 = 8.85 × 10-12 F/ m, Zland) Z, are absolute values of the valances for the two ion types and e is the electron charge e = 1 .602x ! 0-19 C. Given that the bonding force c dE dr an be found as F=-and that at equilibrium interionic dE separation distance the energy has a minimum, 1 e de=0 find the attractive a repulsive force between a K and a Br ion with atomic radii 0.138 and 0.196 nm respectively. Assume that that the ions touch each other at the equilibrium interionic nd separation distance. (20 poir

Explanation / Answer

given
E = Er + Ea = B/r^n - A/r
A = (|z1| + |z2|)e/4*pi*epsilon
epsilon = 8.85*10^-12 F/m
e = 1.602*10^-19 C

now, dE/dr = -nB/r^(n-1) + A/r^2
at equilibrium
attractive force = repulsive force
attractive force = A/r^2
|z1| = 19
|z2| = 35
hence
A = 7.75872*10^-8

hence
attractive force = repulsive force = A/r^2
r = 0.138 + 0.196 nm
F = 6.955*10^11 N

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