To determine the order of ionic character among $$CaH$_2,$ BeH$_2,$ and $$BaH$_2,$ we need to consider the concept of ionic and covalent bonding.$\\$The ionic character of a compound is influenced by the difference in electronegativity between the elements involved.$\\$In general, the greater the difference in electronegativity, the more ionic the bond.$\\$For metal hydrides, the ionic character increases with the size of the metal cation.$\\$This is because larger cations have lower electronegativity, leading to a greater difference in electronegativity with hydrogen.$\\$Let's analyze the given hydrides:$\\$• $$BeH$_2:$ Beryllium is a small cation with relatively high electronegativity among the alkaline earth metals.$\\$• $$CaH$_2:$ Calcium is larger than beryllium and has lower electronegativity.$\\$• $$BaH$_2:$ Barium is even larger than calcium and has the lowest electronegativity among the three.$\\$Thus, the order of increasing ionic character is determined by the size of the metal cation:$\\$BeH$_2 <$CaH$_2 <$BaH$_2 \\$Therefore, the correct order of ionic character is:$\\$Option 3: $$BeH$_2 <$CaH$_2 <$BaH$_2 \\$