Animated Solution for Chemistry - Periodicity in Properties: The correct order of the atomic radii of C, Cs, Al and S is

Mastering Atomic Radii

When we look at the periodic table, it isn't just a random grid of letters and numbers; it is a beautifully orchestrated map of atomic properties. One of the most fundamental properties we can deduce from an element's position is its atomic radius. In this problem, we are tasked with arranging four distinct elements—Carbon ($C$), Cesium ($Cs$), Aluminum ($Al$), and Sulfur ($S$)—in increasing order of their atomic sizes.

To solve this, we don't need to memorize exact picometer values. We just need to understand the two golden rules of the periodic table.

Rule 1: The Period Trend (Left to Right) As we move from left to right across a period, electrons are added to the same principal energy level (shell). Simultaneously, protons are being added to the nucleus. This increases the effective nuclear charge ($Z_{\text{eff}}$). The stronger positive charge from the nucleus pulls the electron cloud closer, causing the atomic radius to decrease.

Rule 2: The Group Trend (Top to Bottom) As we move down a group, an entirely new principal energy level (shell) is added to the atom. Even though the nuclear charge is increasing, the addition of a new shell physically expands the atom's boundary. Furthermore, the inner shells shield the outermost electrons from the nucleus. Therefore, the atomic radius increases significantly as we go down a group.

Let's locate our four elements and apply these rules:

1. Carbon ($C$): Located in Period 2, Group 14. It only has two electron shells. Because it has the fewest shells among our given elements, it is undoubtedly the smallest.

2. Aluminum ($Al$) and Sulfur ($S$): Both are located in Period 3, meaning they both have three electron shells. They will both be larger than Carbon. But how do they compare to each other? Aluminum is in Group 13, while Sulfur is further to the right in Group 16. According to our first rule, the effective nuclear charge increases across the period. Therefore, the nucleus of Sulfur pulls its electrons in tighter than Aluminum does. This makes Sulfur smaller than Aluminum ($r_S<r_{Al}$).

3. Cesium ($Cs$): Located way down in Period 6, Group 1. It has a massive six electron shells! The sheer number of shells makes it a giant compared to the others. It is the largest element in our list.

Putting all our logical deductions together, we can confidently arrange the elements from smallest to largest:

Carbon (2 shells) is the smallest. Sulfur (3 shells, higher $Z_{\text{eff}}$) is next. Aluminum (3 shells, lower $Z_{\text{eff}}$) follows. Cesium (6 shells) is the largest.

The final increasing order is:

This perfectly matches option (a). By simply understanding the tug-of-war between the number of electron shells and the effective nuclear charge, we can predict the relative sizes of almost any elements on the periodic table!