To determine the correct stability order of \( KO_2 \), \( RbO_2 \), and \( CsO_2 \), we need to consider the stability of the superoxide ion (\( O_2^- \)) in these compounds. The stability of the superoxide ion is influenced by the size of the alkali metal cation. Larger cations stabilize the superoxide ion better due to lower charge density and weaker electrostatic attraction.
Stability Trend:
As we move down the alkali metal group (from \( K \) to \( Rb \) to \( Cs \)), the size of the cation increases.
Larger cations (like \( Cs^+ \)) stabilize the superoxide ion (\( O_2^- \)) more effectively than smaller cations (like \( K^+ \)).
Thus, the stability order of the superoxides is:
\[
KO_2<RbO_2<CsO_2
\]
Correct Option:
The correct stability order is:
\[
\boxed{KO_2<RbO_2<CsO_2}
\]
This corresponds to option (4).