Order of successive ionisation enthalpies:  Δ _i H ₁  <  Δ _i H ₂  <  Δ _i H _{3. why is 1st IE less than 2nd and 3rd. grp 15 elements have half filled p orbital so removal of 1st electron must require more energy than removal of progressive electrons. so 1st IE must be greater than 2nd and 3rd.}

The 1st ionisation energy is always less than the subsequent ionisation energies. This is because 1st ionisation energy involves the removal of the most loosely bound electron from a neutral gaseous atom. On the other hand, the subsequent ionisation energies (i.e. 2^nd ionistaion energy, 3^rd ionisation energy etc) involve the removal of an electron from a positively charged cation. The forces of attraction between the nucleus and the outermost electrons in a cation are stronger as compared to an atom because the positive charge is more in cation. So the valence electron(s) in a cation would be held more strongly than in an atom. Hence it would be more difficult to pull out an electron from a positively charged species, and this increases with the increase in positive charge on the cation. 

It is always difficult to remove (and even add) electrons from a half filled or fully filled orbital because of the extra stability associated with them. Therefore the ionisation energy of group 15 elements would be high as they have half filled p orbitals. However, second ionisation energy means removing an electron from a positively charged cation, in which the electrons are held more strongly to the nucleus than in a neutral atom. Therefore the second and the third ionisation energies would be higher than the first.