The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet…

Step 1: Analyze the Borax Bead Test colors

First, let's identify the cation from the given physical observation: "gives a violet colour in non-luminous flame under hot condition in borax bead test".

• $\ce{Cr^{3+}}$: Green (hot and cold)
• $\ce{Mn^{2+}}$: Violet/Amethyst in oxidizing flame (hot and cold)
• $\ce{Ni^{2+}}$: Reddish-brown (cold) and Violet (hot) in an oxidizing (non-luminous) flame. Let's keep both $\ce{Mn^{2+}}$ and $\ce{Ni^{2+}}$ in mind.

Step 2: Analyze the electronic configuration dependency

The question specifies that the electronic configuration of the ion is "not affected by the nature of the ligand". This refers to crystal field pairing depending on whether the ligand is a strong field (SFL) or a weak field ligand (WFL).

• $\ce{Cr^{3+}}$ is a $d^{3}$ system: In octahedral complexes, it always forms $t_{2g}^3 e_g^0$, meaning its configuration is unaffected by the ligand. But its bead test color is green.
• $\ce{Ti^{3+}}$ is a $d^{1}$ system: Its configuration ($t_{2g}^1$) is unaffected by the ligand. But no violet hot bead.
• $\ce{Mn^{2+}}$ is a $d^{5}$ system: In presence of WFL it is high-spin ($t_{2g}^3 e_g^2$), and in presence of SFL it is low-spin ($t_{2g}^5 e_g^0$). So it IS affected by the nature of the ligand.
• $\ce{Ni^{2+}}$ is a $d^{8}$ system: In an octahedral complex, the configuration will always be $t_{2g}^6 e_g^2$ regardless of whether the ligand is strong or weak, because filling 8 electrons leaves exactly two unpaired electrons in the $e_g$ level in either case.

Step 3: Conclusion

Since nickel(II) is a $d^{8}$ system whose octahedral electronic configuration is independent of the ligand's field strength, and it produces a violet borax bead when hot in the oxidizing flame, option (d) is correct.

Key Points to Remember:

• $d^1$, $d^2$, $d^3$, $d^8$, $d^9$ electronic configurations in octahedral complexes do not change with the field strength of ligands.
• $d^4$, $d^5$, $d^6$, $d^7$ configurations vary depending on Strong Field vs Weak Field ligands.
• Nickel ($\ce{Ni^{2+}}$) borax bead test: Oxidizing flame is reddish-brown cold and violet hot.