Animated Solution for Chemistry - Periodicity in Properties: The first ionisation energy of magnesium is smaller as compared to that of elements $X$ and $Y$, but higher than that of $Z$. The elements $X$, $Y$ and $Z$, respectively, are

The Magnesium Anomaly

Ionisation energy is one of those periodic properties that seems straightforward at first glance but is packed with fascinating quantum mechanical traps. In this problem, we are tasked with finding three elements ($X$, $Y$, and $Z$) based on their first ionisation energy relative to Magnesium. Specifically, we need $IE(Z)<IE(\text{Mg})<IE(X),IE(Y)$.

Quantum Reality

The general rule of thumb is simple: as you move from left to right across a period, the effective nuclear charge ($Z_{\text{eff}}$) increases. The nucleus pulls the outermost electrons more tightly, shrinking the atomic radius and making it harder to remove an electron. Therefore, ionisation energy generally increases from left to right.

However, quantum mechanics loves to throw a wrench into simple linear trends. Magnesium is a Group 2 element with an atomic number of 12. Its electronic configuration is $[\text{Ne}]3s^2$. Notice that the $3s$ subshell is fully filled. This paired state is highly stable.

If we look at its neighbor to the right, Aluminum (Group 13), its configuration is $[\text{Ne}]3s^{2}3p^1$. Removing the lone, slightly higher-energy $3p$ electron from Aluminum is actually easier than breaking the stable $3s^2$ pair in Magnesium. Thus, we get our first anomaly: $IE(\text{Mg})>IE(\text{Al})$.

If we plot the actual first ionisation energies for the 3rd period, we see two distinct dips (at Group 13 and Group 16). The complete, correct sequence from lowest to highest energy is:

Now, let's apply our conditions to this sequence. We need an element $Z$ that has a lower ionisation energy than Magnesium. Looking at our sequence, only Sodium (Na) and Aluminum (Al) fit this description.

Next, we need elements $X$ and $Y$ that have a higher ionisation energy than Magnesium. The elements to the right of Magnesium in our sequence (Si, S, P, Cl, Ar) all satisfy this condition.

Let's evaluate the given options: - Option (a): Cl, Li, Na. (Lithium is in the 2nd period and its IE is actually lower than Mg. Incorrect.) - Option (b): Ar, Li, Na. (Again, Lithium ruins it.) - Option (c): Ar, Cl, Na. Here, $X=\text{Ar}$ and $Y=\text{Cl}$ (both have higher IE than Mg), and $Z=\text{Na}$ (has lower IE than Mg). This is a perfect match! - Option (d): Ne, Na, Cl. (Neon is a 2nd period noble gas with a massive IE, but the order $X,Y,Z$ requires $Y$ to be greater than Mg, and Na is not. Incorrect.)

Therefore, the correct elements are Argon, Chlorine, and Sodium. Always remember to map out the exact sequence with exceptions before jumping into the options!