In my textbook it is written that ionisation energy and ionisation enthalpy are two different quantities. ionisation energy is the amount of energy provided to extract an electron from the outermost shell of a neutral or ionic gaseous atom and ionisation enthalpy is the change in energy of the 1 mole of gaseous atoms or ions when the outermost electron is removed from the atoms or ions. Since electron is in bounded state in an atom so the net potential energy of the electron nucleus system is negative and to free up the electron from the bounded system we need to change the negative potential energy of the system to zero or positive value by providing an extra amount of energy from our side which is called ionisation energy and since we are PROVIDING the energy mathematically it is written with the positive sign (by definition of ionisation energy), ionisation energy is always positive. But ionisation enthalpy is something different it is the difference in the energy of the state of the system before and after ionisation it can be positive or negative depending on the stability of product with respect to reactant. The question arises here is that are ionisation energy and ionisation enthalpy same in the magnitude.