Step 1: Energy levels in lanthanoids. In lanthanoids, the $4f$ orbital is deeply embedded and well shielded. The energy gap between $4f$ and $5d$ orbitals is relatively large, so $4f$ electrons participate only to a limited extent in bonding. Lanthanoids predominantly show the $+3$ oxidation state. Step 2: Energy levels in actinoids. In actinoids, the $5f$, $6d$, and $7s$ orbitals have very similar and closely spaced energies. Electrons can readily be involved from any of these sublevels in bonding. Step 3: Variable oxidation states. Because $5f$, $6d$, and $7s$ electrons all participate in bonding, actinoids show a wide range of oxidation states from $+3$ up to $+7$. This variability makes their chemistry far more complex than lanthanoids. Step 4: Additional complication. All actinoids are radioactive, and many heavier actinoids are synthetic transuranium elements available only in tiny amounts. The chemistry of actinoids is more complicated because comparable energies of $5f$, $6d$, and $7s$ orbitals lead to variable oxidation states ($+3$ to $+7$), and all actinoids are radioactive.
