(i) Variation of atomic radii across a series:
Across a transition series, atomic radii decrease slightly from left to right. This happens because as we move across the period, the nuclear charge increases due to the addition of protons.
However, the added electrons enter the penultimate \((n-1)d)\) orbital, providing poor shielding of the outer electrons. Thus, the increased nuclear charge pulls electrons closer, reducing atomic size.
After the mid-series, the effect of electron-electron repulsion in the \(d\)-orbitals balances the nuclear pull, so the decrease becomes very small.
(ii) Paramagnetic nature of transition metal ions:
Transition metal ions generally contain unpaired electrons in their \((n-1)d)\) orbitals.
Paramagnetism arises due to the presence of these unpaired electrons, which have magnetic moments associated with their spins. Hence, most transition metal ions exhibit paramagnetism.
(iii) Variable oxidation states in transition elements:
Transition elements show variable oxidation states because the energy difference between the \((n-1)d)\) and \(ns\) orbitals is very small.
As a result, both \(ns\) and \((n-1)d)\) electrons can take part in bonding.
Thus, transition metals can exhibit multiple oxidation states (e.g., Fe shows +2 and +3, Mn shows +2 to +7).
Conclusion:
The unique electronic configuration of transition metals (\((n-1)d^{1-10}ns^{0-2}\)) explains their small variation in radii, paramagnetism, and variable oxidation states.