Born-Haber Cycle: Formation of a Chlorine Atom

[henry3369]

Homework Statement

I don't actually need help with an entire problem, I just can't seem to figure out what goes on when an atom is formed from a molecule in a Born-Haber cycle.

For example:
The formation of a chlorine atom from a chlorine molecule
(1/2)Cl₂ → Cl(g) ΔH = (1/2) x bond energy of Cl₂ = +122 kJ

Homework Equations

The Attempt at a Solution

Why is the bond energy being halved? It you have a Cl₂ molecule, and you need 244 kJ to break the bond into two Cl atoms. Why would the formation of a Cl atom be only half of that then?

 

[paisiello2]

Doesn't that (1/2) factor mean something?

 

[Ygggdrasil]

Here, it might be more useful to think in terms of moles. Reacting one mole of Cl2 takes 244 kJ, and making one mole of chlorine atoms requires reacting 0.5 moles of Cl2.