Let's break down each option one by one to identify the one that does not represent the correct property.
Option (A) $ \text{CO}^{2+} < \text{Fe}^{2+} < \text{Mn}^{2+} $ – Ionic size:
The ionic size generally increases with the increasing atomic number when ions are in the same oxidation state.
- $ \text{CO}^{2+} $ has the smallest ionic radius, followed by $ \text{Fe}^{2+} $, and then $ \text{Mn}^{2+} $.
- This order is correct for ionic sizes, so option (A) is correct.
Option (B) $ \text{Ti} < \text{V} < \text{Mn} $ – Number of oxidation states:
- Titanium (Ti) typically has oxidation states of +2 and +4.
- Vanadium (V) can exhibit +2, +3, +4, and +5 oxidation states.
- Manganese (Mn) shows a broader range of oxidation states from +2 to +7.
- The increasing number of oxidation states from Ti to Mn is correct. Therefore, option (B) is correct.
Option (C) $ \text{Cr}^{2+} < \text{Mn}^{2+} < \text{Fe}^{2+} $ – Paramagnetic behavior:
- $ \text{Cr}^{2+} $ has 4 unpaired electrons, $ \text{Mn}^{2+} $ has 5 unpaired electrons, and $ \text{Fe}^{2+} $ has 4 unpaired electrons.
- This order is consistent with paramagnetic behavior, where more unpaired electrons correspond to stronger paramagnetism.
- Therefore, option (C) is correct.
Option (D) $ \text{Sc} > \text{Cr} > \text{Fe} $ – Density:
- The density of Scandium (Sc) is about 2.985 g/cm³, Chromium (Cr) is about 7.19 g/cm³, and Iron (Fe) is about 7.87 g/cm³.
- This shows that the density of Fe is higher than Cr, and Cr is higher than Sc, which makes the order $ \text{Sc} > \text{Cr} > \text{Fe} $ incorrect.
- Therefore, option (D) is incorrect.
Conclusion:
The correct answer is (D), as it does not represent the correct order of density for the given elements.
Let's evaluate each option:
The correct answer is (D) : Sc > Cr > Fe - Density.