What are the formulae of the compounds formed when lanthanoids (Ln) react with nitrogen and halogen respectively?
Show Hint
Remember that the general chemistry of lanthanoids is governed by their most common and stable oxidation state, which is $+3$. Simply balancing this charge with standard anions ($\text{N}^{3-}$ and $\text{X}^-$) quickly yields the correct chemical formulas.
Step 1: Read what the question wants.
We must write the formula of the compound a lanthanoid metal makes with nitrogen, and the formula it makes with a halogen like chlorine or fluorine. Here Ln stands for any lanthanoid and X stands for any halogen.
Step 2: Recall the favourite charge of lanthanoids.
All lanthanoids love to lose three electrons and sit as a $+3$ ion. So we treat the metal as $\text{Ln}^{3+}$ in almost every compound. This is the single most useful fact for this question.
Step 3: Find the charge on nitrogen.
Nitrogen is in group 15. When it acts as a simple anion it gains three electrons and becomes the nitride ion $\text{N}^{3-}$. So its charge is $-3$.
Step 4: Combine metal and nitrogen.
A compound must be electrically neutral, so the plus and minus charges have to cancel. Here $+3$ from the metal exactly cancels $-3$ from nitrogen, so we need just one of each.
\[ \text{Ln}^{3+} + \text{N}^{3-} \rightarrow \text{LnN} \]
Step 5: Find the charge on a halogen and combine.
A halogen gains one electron and becomes $\text{X}^-$, charge $-1$. To balance one $+3$ metal ion we need three of these $-1$ ions.
\[ \text{Ln}^{3+} + 3\text{X}^- \rightarrow \text{LnX}_3 \]
Step 6: Match with the options.
So the two formulas are LnN and $\text{LnX}_3$. This matches option 1. The trick in every wrong option is using the wrong charge for the metal or the halogen.
\[ \boxed{\text{LnN and } \text{LnX}_3} \]