Age 16 to 18 Challenge Level:
Having constructed the Born-Haber cycles, and having worked out the
relevant data, look at how the two cycles differ. There should be
one key point that changed enormously, to make the formation of
NaCl$_2$ so unfavourable. Think what the change would be for a
NaCl$_3$, and whether this would be offset by the lattice enthalpy.
Generally, we can draw a conclusion for NaCl$_n$...
Although the Born-Lande equation will be new to almost everyone,
this question involves little more than plugging in given data to
the equation. Note that the Born-Lande calculates lattice
enthalpies based on a purely electrostatic model, and consequently
always underestimates the true lattice enthalpy. What extra factor
hasn't been taken into account? Why would this factor increase for