Q.Define Lanthanide contraction. Write the balanced chemical equations when acidified K$_2$Cr$_2$O$_7$ reacts with H$_2$S.

Atomic radii of transition elements decrease gradually moving left to right across a series, because nuclear charge rises steadily while each newly-added electron enters the same, already partly-filled (n-1)d subshell rather than a fresh outer shell; since d orbitals are diffuse and poorly-penetrating, d electrons shield the growing nuclear charge from each other only weakly, so effective nuclear charge climbs steadily and pulls the electron cloud progressively inward. Ionic radii follow the same underlying logic and can be examined two ways: for a FIXED oxidation state, ionic radius decreases across the row as nuclear charge rises (most cleanly seen for divalent ions, e.g. Cr2+ 82pm vs Cu2+ 73pm); and for a GIVEN element, ionic radius decreases going from a lower to a higher oxidation state (M2+ to M3+), since removing more electrons raises the effective nuclear charge on those remaining. The identical mechanism -- poor shielding by a diffuse, partly-filled inner sub …