Animated Solution for Chemistry - Periodicity in Properties: Which of the following represents the correct order of increasing first ionisation enthalpy for Ca, Ba, S, Se and Ar ?

Imagine you are trying to take a toy away from a child. The closer the child holds the toy, and the stronger the child is, the harder it is to pull that toy away. In the atomic world, this "toy" is the outermost electron, and the energy required to snatch it away is called the First Ionisation Enthalpy (${\Delta }_i{H}_1$).

In this classic JEE problem, we are tasked with arranging five elements—Calcium ($\text{Ca}$), Barium ($\text{Ba}$), Sulphur ($\text{S}$), Selenium ($\text{Se}$), and Argon ($\text{Ar}$)—in increasing order of their ionisation enthalpy. To solve this, we don't need to memorize exact values; we just need to understand the rhythm of the periodic table.

Before we look at the specific elements, let's establish the ground rules. The periodic table has two main directions of travel, and each dictates how tightly electrons are held:

1. Across a Period (Left to Right): As we move across a period, electrons are added to the same shell, but the nucleus gains more protons. This increases the effective nuclear charge ($Z_{\text{eff}}$). The nucleus pulls the electron cloud closer and tighter. Consequently, it becomes much harder to remove an electron, meaning the ionisation enthalpy increases.

2. Down a Group (Top to Bottom): As we descend a group, entirely new electron shells are added. The outermost electrons are now further away from the nucleus and are shielded by the inner layers of electrons. Because the distance is greater and the pull is weaker, it is easier to pluck an electron away. Thus, the ionisation enthalpy decreases.

To apply these rules, we must first locate our elements on the periodic table grid. Visualizing their coordinates is half the battle won!

Group 2 (Alkaline Earth Metals): We have Calcium ($\text{Ca}$) in Period 4 and Barium ($\text{Ba}$) way down in Period 6. Group 16 (Chalcogens): We have Sulphur ($\text{S}$) in Period 3 and Selenium ($\text{Se}$) just below it in Period 4. Group 18 (Noble Gases):* We have Argon ($\text{Ar}$) sitting proudly in Period 3.

Now, let's break the comparison down into bite-sized atomic computations.

Comparing the Metals (Group 2): Between Calcium and Barium, Barium is located further down the group. It has more shells, making its atomic radius significantly larger. The outermost electrons in Barium are far from the nucleus and heavily shielded. Therefore, it requires less energy to remove an electron from Barium than from Calcium.

Comparing the Non-Metals (Group 16 & 18): Moving to the right side of the periodic table, we look at Sulphur and Selenium. Selenium is below Sulphur in Group 16. By the exact same logic we used for the metals, Selenium's larger size means it has a lower ionisation enthalpy than Sulphur.

What about Argon? Argon is a noble gas. It possesses a fully filled, highly stable octet configuration ($n{s}^{2}n{p}^6$). It is extremely reluctant to disrupt this perfect stability by losing an electron. Therefore, Argon will have the highest ionisation enthalpy of all the elements listed.

Piecing it Together: Metals on the far left generally have much lower ionisation enthalpies than non-metals on the right. So, our Group 2 elements will have lower values than our Group 16 elements, and the Group 18 noble gas will top the chart.

Combining our inequalities, we get the final increasing order:

This perfectly matches option (c).

While the general trends of atomic size and nuclear charge perfectly solved this problem, always stay alert for the JEE's favorite traps: electronic configuration exceptions.

For example, if you were asked to compare Nitrogen (Group 15) and Oxygen (Group 16), the general left-to-right trend suggests Oxygen should have a higher ionisation enthalpy. However, Nitrogen has a perfectly half-filled $2p$ subshell ($2p^3$), which grants it extra stability. Thus, Nitrogen actually has a higher first ionisation enthalpy than Oxygen! Always check the orbital configurations when comparing adjacent elements in the same period.