Answer: Calculating Lattice Binding Energy of MgO Crystal

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SUMMARY

The discussion focuses on calculating the total binding energy of the magnesium ion (Mg) in a magnesium oxide (MgO) crystal lattice, where Mg is surrounded by six oxygen (O) ions. The participant, Sean, utilizes the Coulombic force equation, F_c = -K/a^2, to determine the attractive force at equilibrium bond length but struggles with the concept of net force being zero, leading to confusion about the binding energy being sought. The conclusion is that the question pertains to the total binding energy of the Mg ion, not the electron binding energy.

PREREQUISITES
  • Understanding of Coulomb's Law and its application in ionic interactions.
  • Familiarity with crystal lattice structures, specifically the arrangement of ions in MgO.
  • Knowledge of equilibrium bond lengths and ionic radii.
  • Basic principles of force balance in physical systems.
NEXT STEPS
  • Research the calculation of lattice energy using the Born-Haber cycle.
  • Study the concept of ionic bonding and its implications in crystal structures.
  • Explore the relationship between ionic radii and bond lengths in ionic compounds.
  • Learn about the role of attractive and repulsive forces in determining stability in ionic lattices.
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Students in chemistry or materials science, particularly those studying ionic compounds and crystal lattice structures, as well as educators looking for examples of lattice energy calculations.

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Homework Statement



In a crystal lattice of MgO, the Mg is surrounded by 6 Oxygen atoms as shown.
Assume that the ions all behave as point charges.

If the system behaves as though there were separate interactions between Mg and each of
the Oxygen ions what is the total binding energy of the Mg ion?

Homework Equations



F_c = -K/a^2
F=\frac{dE}{da}
F=F_c+F_R


The Attempt at a Solution



so I'm quite confused with this question.

I can find the coulombic force of attraction using F_c = -K/a^2 if i take a to be the equilibrium bond length and look up values for the ionic radii.

Now that i know the attraction force i can then work out the repulsive force as at the equilibrium bond length the attractive force is balanced by the repulsive force.

my problem is that because the forces balance the net force is zero , so what is the total binding energy of the iron.
 
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would anyone agree that the question is asking for the electron binding energy and that i was trying to find the wrong thing?

im still stuck with this.

Thanks
Sean
 

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