Question

When magnesium is ignited in air, the magnesium reacts with oxygen and nitrogen.

Answer 1

51: The only coefficient is in the first one i think and it would be a 3
52: Neon (Ne)
53: Mg has a low nuclear charge so all it's electrons would be lost in the electron shell, making the ion smaller than the atom.

Answer 2

51)

Mg(s) + N₂(g) --> Mg₃N₂(s)

There is one Mg atom on the reactant side and three Mg atoms on the product side. So to balance the number of Mg on both side of the equation a coefficient 3 is placed before Mg on the reactant side. The number of N atoms are two on both side of the reaction. Therefore the balanced chemical equation is,  

2Mg(s) + N₂(g) --> Mg₃N₂(s)

52)

The electron configuration of Mg is 1s²2s²2p⁶3s² or [Ne]3s²

The electron configuration of Mg²⁺ is 1s²2s²2p⁶ or [Ne]

The electron configuration of Ne is 1s²2s²2p⁶

Ne he same electron configuration as a Mg²⁺ ion.

53)

Mg has its valence electron in the 3s shell, but Mg²⁺ has no electron in the 3s shell, the valence electron in Mg²⁺is in the 2p orbital. The size of the 2 shell is smaller than the 3 shell. Hence, Mg²⁺ is smaller than Mg.