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The salt of \(Sc^{3+}\) ion is colourless and the salt of \(Mn^{3+}\) ion is coloured. Explain. [Z of Sc = 21 and Z of Mn = 25]

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Any ion with \(d^0\) or \(d^{10}\) configuration is colourless. Ions with \(d^1\) to \(d^9\) configurations are typically coloured.
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Solution and Explanation

Step 1: Understanding the Concept:
The color of transition metal ions is generally due to \(d-d\) electronic transitions. For such transitions, the metal ion must have a partially filled \(d\)-orbital (\(d^1\) to \(d^9\)).
Step 3: Detailed Explanation:
1. \(Sc^{3+}\) ion:
Configuration of \(Sc\) (\(Z=21\)): \([Ar] 3d^1 4s^2\).
Configuration of \(Sc^{3+}\): \([Ar] 3d^0\).
Since there are no electrons in the \(d\)-orbital, \(d-d\) transitions are impossible. Hence, its salts are colourless.
2. \(Mn^{3+}\) ion:
Configuration of \(Mn\) (\(Z=25\)): \([Ar] 3d^5 4s^2\).
Configuration of \(Mn^{3+}\): \([Ar] 3d^4\).
It has 4 unpaired electrons in the \(3d\) subshell. When light falls on the salt, electrons can jump between split \(d\)-orbitals (\(d-d\) transition), absorbing specific wavelengths and reflecting the rest. Thus, it is coloured (typically violet/purple).
Step 4: Final Answer:
\(Sc^{3+}\) is \(3d^0\) (colourless) and \(Mn^{3+}\) is \(3d^4\) (coloured).
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