1. Given comparison

We need elements $X, Y, Z$ such that the first ionization energy of magnesium satisfies:

$IE_1(\text{Mg}) < IE_1(X), \quad IE_1(\text{Mg}) < IE_1(Y), \quad IE_1(\text{Mg}) > IE_1(Z)$

So both $X$ and $Y$ must have higher first ionization energy than Mg, while $Z$ must have lower first ionization energy than Mg.

2. Recall periodic trend

• Ionization energy generally increases across a period from left to right.
• Ionization energy generally decreases down a group.
• Magnesium is in Period 3, Group 2.

Approximate relative order among relevant elements:

$\text{Na} < \text{Mg} < \text{Cl} < \text{Ar} < \text{Ne}$

Also, lithium is above sodium in Group 1, so:

$IE_1(\text{Li}) > IE_1(\text{Na})$

And comparing Li with Mg, magnesium has higher first ionization energy than lithium:

$IE_1(\text{Li}) < IE_1(\text{Mg})$

3. Check each option

Option A: $X=\text{Ne},\ Y=\text{Na},\ Z=\text{Cl}$

Need:

• $IE(\text{Ne}) > IE(\text{Mg})$ ✅
• $IE(\text{Na}) > IE(\text{Mg})$ ❌ since $IE(\text{Na}) < IE(\text{Mg})$
• $IE(\text{Cl}) < IE(\text{Mg})$ ❌ since $IE(\text{Cl}) > IE(\text{Mg})$

So A is incorrect.

Option B: $X=\text{Ar},\ Y=\text{Cl},\ Z=\text{Na}$

Check:

• $IE(\text{Ar}) > IE(\text{Mg})$ ✅
• $IE(\text{Cl}) > IE(\text{Mg})$ ✅
• $IE(\text{Na}) < IE(\text{Mg})$ ✅

So B is correct.

Option C: $X=\text{Cl},\ Y=\text{Li},\ Z=\text{Na}$

Check:

• $IE(\text{Cl}) > IE(\text{Mg})$ ✅
• $IE(\text{Li}) > IE(\text{Mg})$ ❌ actually $IE(\text{Li}) < IE(\text{Mg})$
• $IE(\text{Na}) < IE(\text{Mg})$ ✅

So C is incorrect.

Option D: $X=\text{Ar},\ Y=\text{Li},\ Z=\text{Na}$

Check:

• $IE(\text{Ar}) > IE(\text{Mg})$ ✅
• $IE(\text{Li}) > IE(\text{Mg})$ ❌
• $IE(\text{Na}) < IE(\text{Mg})$ ✅

So D is incorrect.

4. Final answer

The correct set is:

$X=\text{Ar},\quad Y=\text{Cl},\quad Z=\text{Na}$

So the correct option is B.