born haber cycle is based on Hess law?

Yes, Born haber cycle is based on Hess low.

Hess’s   law of constant heat summation: When a reaction takes place in several steps, its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.

 An application of this law is Born-Haber cycle:

Born-Haber cycle can be used to calculate the lattice enthalpy of an ionic compound, from the enthalpies of the various steps involved in the formation of ionic compound. Let us consider the formation of NaCl, and see how lattice enthalpy of NaCl can be calculated using Born-Haber cycle:

In this example, enthalpy of formation of NaCl is calculated using Born-Haber cycle. Here, U is the lattice enthalpy of NaCl, if all the other values are provided, then we can use the above equation to calculate U.

In this example, enthalpy of formation of NaCl is calculated using Born-Haber cycle. Here, U is the lattice enthalpy of NaCl, if all the other values are provided, then we can use the above equation to calculate U.