Identify the elements X and Y using the ionization energy values given below: | | 1st IE | 2nd IE | |---|---|---| | X |…

🧠 Ratio of $IE_2/IE_1$ tells you exactly when the noble-gas core is reached. Group 1 elements show a huge jump (~9×). Group 2 elements show only a small jump (~2×) When you remove a valence electron and the next one must come from a noble-gas core, the energy needed jumps enormously — easily by a factor of 5-10. So tracking the IE ratios reveals which group an element belongs to.

🗺️ Read the data Element X: $IE_1 = 495$, $IE_2 = 4563$. Ratio $\approx 9.2$. A huge jump means the second electron came from the noble-gas core. So X had only 1 valence electron → Group 1. The Group 1 element with $IE_1 \approx 495\,kJ/mol$ is Na ($IE_1$ tabulated = 496).

Element Y: $IE_1 = 731$, $IE_2 = 1450$. Ratio $\approx 2$. Both electrons came from the same valence shell. So Y had 2 valence electrons → Group 2. The Group 2 element with $IE_1 \approx 731\,kJ/mol$ is Mg ($IE_1$ tabulated = 737).

So X = Na and Y = Mg.

⚠️ The trap Students sometimes pick option (c) X = Mg, Y = Na — flipping the labels. The fix is to always look at the ratio first, not the absolute values. A 9× jump → Group 1 → Na. A 2× jump → Group 2 → Mg. The ratio is the diagnostic, not the raw numbers.

$\boxed{\text{Answer: (a)}}$