The borax bead test is given by transition metal ions that have unpaired electrons and form coloured compounds.
Zn2+ has a completely filled 3d10 configuration, making it colourless, so it does not give a positive borax bead test.
The remaining ions and their electronic configurations are:
Fe2+:[Ar]3d6
Cr2+:[Ar]3d4
Fe3+:[Ar]3d5
The ionisation enthalpy of an ion refers to the energy required to remove an electron from it. Fe3+ has a highly stable half-filled d-subshell configuration (3d5). Removing an electron from this stable configuration requires significantly more energy compared to removing an electron from Fe2+ (3d6) or Cr2+ (3d4).
Therefore, Fe3+ shows a positive borax bead test and has the highest ionisation enthalpy among the given ions.
Answer: Fe3+