The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet color in non-luminous flame under hot condition in borax bead test is:
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The borax bead test is useful for detecting certain metal ions in compounds due to characteristic colors they produce when heated in borax.
Chromium(III) ion (Cr$^{3+}$) typically maintains its electronic configuration across different complexes and imparts a violet color in the borax bead test, a characteristic of Cr$^{3+}$ due to its specific electron configuration.