What happens when magnesium is burnt in air and the products $X$ and $Y$ are treated with water?
\[\begin{align}
  & Mg\xrightarrow[Air]{\Delta }X+Y \\
 & X\xrightarrow{{{H}_{2}}O}P \\
 & Y\xrightarrow{{{H}_{2}}O}P+Q \\
\end{align}\]
A. $X-MgO$, $Y-Mg{{(OH)}_{2}}$, $P-Mg{{(OH)}_{2}}$, $Q-{{N}_{2}}$
B. $X-MgO$, $Y-M{{g}_{3}}{{N}_{2}}$, $P-Mg{{(OH)}_{2}}$, $Q-N{{H}_{3}}$
C. $X-MgO$, $Y-M{{g}_{3}}{{N}_{2}}$, $P-Mg{{(OH)}_{2}}$, $Q-{{N}_{2}}$
D. $X-MgO$, $Y-MgC{{O}_{3}}$, $P-Mg{{(OH)}_{2}}$, $Q-C{{O}_{2}}$

Hint: Think about the composition of air, the reaction includes the two main constituents of air. Then think about what might happen once the compounds react with water and you will arrive at your answer.

Complete step by step solution:
The two main constituents of air are $N$ and $O$. Thus, when an $Mg$ribbon is burned in air. A reaction occurs that involves $Mg$,$N$, and $O$.
The reactions that occur are:
2 moles of magnesium combine with 1 mole of oxygen to give 2 moles of magnesium oxide.
\[2Mg+{{O}_{2}}\xrightarrow{\Delta }2MgO\]
3 moles of magnesium combine with 1 mole of nitrogen to give 1 mole of magnesium nitride.
\[3Mg+{{N}_{2}}\xrightarrow{\Delta }M{{g}_{3}}{{N}_{2}}\]
This tells us that the answer is amongst option B. and option C.
When magnesium oxide reacts with water magnesium hydroxide is formed.
$MgO+{{H}_{2}}O\xrightarrow{{}}Mg{{(OH)}_{2}}$
Magnesium nitride undergoes a double displacement reaction with 6 moles of water to form 3 moles of magnesium hydroxide and 2 moles of ammonia.
\[M{{g}_{3}}{{N}_{2}}+6{{H}_{2}}O\xrightarrow{{}}3Mg{{(OH)}_{2}}+2N{{H}_{3}}\]
Thus, $P-Mg{{(OH)}_{2}}$and $Q-N{{H}_{3}}$
Hence, the answer is ‘B. $X-MgO$, $Y-M{{g}_{3}}{{N}_{2}}$, $P-Mg{{(OH)}_{2}}$, $Q-N{{H}_{3}}$’.

Additional information:
The 2 reactions involving oxygen are both additional reactions. In the reactions involving nitrogen, the first reaction is an additional reaction while the second one is a double displacement reaction.
Magnesium only combines with oxygen and nitrogen when ignited, it burns with a bright, white flame which may be blinding if you look at it directly. Always be careful if this experiment is carried out in front of you.
Note:The reaction $M{{g}_{3}}{{N}_{2}}+6{{H}_{2}}O\xrightarrow{{}}3Mg{{(OH)}_{2}}+2N{{H}_{3}}$ is not the only one that occurs.
Sometimes, under specific conditions, magnesium nitride may combine with 3 moles of water to give 3 moles of magnesium oxide and 2 moles of ammonia.
\[M{{g}_{3}}{{N}_{2}}+3{{H}_{2}}O\xrightarrow{{}}3MgO+2N{{H}_{3}}\]
But since none of the options in this question include this combination, we can ignore this reaction here.