Identify Ion Showing Positive Borax Bead Test and Highest Ionisation Enthalpy

To determine which ion shows a positive borax bead test and has the highest ionisation enthalpy among $\text{Fe}^{2+}$, $\text{Fe}^{3+}$, $\text{Cr}^{2+}$, and $\text{Zn}^{2+}$, we evaluate both criteria:

1. Borax Bead Test:

• The borax bead test is a qualitative analysis used to identify certain metal cations based on the characteristic colors produced by their metaborates in oxidizing and reducing flames.
• Transition metal ions with partially filled $d$-orbitals exhibit $d$-$d$ transitions and yield characteristic colored beads:
  • $\text{Fe}^{3+}$ gives a characteristic yellow/brown bead in an oxidizing flame and a bottle-green bead in a reducing flame.
  • $\text{Fe}^{2+}$ and $\text{Cr}^{2+}$ also give positive (colored) borax bead tests.
  • $\text{Zn}^{2+}$ has a completely filled $d$-subshell ($3d^{10}$) and forms a colorless bead, failing to give a positive colored borax bead test.

2. Ionisation Enthalpy:

• The ionisation enthalpy of an ion increases with an increase in effective nuclear charge ($Z_{\text{eff}}$) and positive oxidation state.
• Comparing the given species:
  • $\text{Cr}^{2+}$: $[\text{Ar}]\, 3d^4$
  • $\text{Fe}^{2+}$: $[\text{Ar}]\, 3d^6$
  • $\text{Zn}^{2+}$: $[\text{Ar}]\, 3d^{10}$
  • $\text{Fe}^{3+}$: $[\text{Ar}]\, 3d^5$
• Among the given options, $\text{Fe}^{3+}$ carries the highest positive charge ($+3$), resulting in the smallest ionic radius and maximum effective nuclear charge $Z_{\text{eff}}$ acting on the valence electrons. Furthermore, $\text{Fe}^{3+}$ possesses a highly stable half-filled $3d^5$ electronic configuration.
• Consequently, removing an electron from $\text{Fe}^{3+}$ requires the highest amount of energy, giving it the highest ionisation enthalpy among all four options.

Combining both criteria, $\text{Fe}^{3+}$ is the ion that gives a positive borax bead test and possesses the highest ionisation enthalpy.

Correct Answer: D ($\text{Fe}^{3+}$)