To determine the simplest formula for the ionic compound formed between magnesium and element $X,$ we first need to analyze the electronic configuration of $X. \\$Given:$\\$• The ground state electronic configuration of $X$ is $1s^2 2s^2 2p^3. \\$This configuration corresponds to nitrogen (N), which is in Group 15 of the periodic table.$\\$• Nitrogen has 5 valence electrons and needs 3 more electrons to achieve a stable octet configuration.$\\$Magnesium (Mg) has the electronic configuration $1s^2 2s^2 2p^6 3s^2. \\$• Magnesium has 2 valence electrons and tends to lose these 2 electrons to achieve a stable configuration.$\\$To form an ionic compound:$\\$• Magnesium will lose 2 electrons to form $Mg^{2+}. \\$• Nitrogen will gain 3 electrons to form $N^{3-}. \\$To balance the charges in the compound:$\\$• We need 3 magnesium ions to balance the charge of 2 nitrogen ions.$\\$• This results in the formula $Mg_3N_2. \\$Therefore, the simplest formula for the compound is $Mg_3N_2. \\$This corresponds to Option 4.