Use periodic trends of atomic radius

Atomic radius generally:

• decreases across a period from left to right
• increases down a group from top to bottom

Locate the elements in the periodic table

• $\mathrm{C}$ : Period 2, Group 14
• $\mathrm{S}$ : Period 3, Group 16
• $\mathrm{Al}$ : Period 3, Group 13
• $\mathrm{Cs}$ : Period 6, Group 1

Compare $\mathrm{Al}$ and $\mathrm{S}$

Both are in Period 3. Across a period, radius decreases from left to right. Since $\mathrm{Al}$ is to the left of $\mathrm{S}$, $\mathrm{Al} > \mathrm{S}$

Compare $\mathrm{Cs}$ with all others

$\mathrm{Cs}$ is in Period 6 and Group 1, so it has the largest atomic radius among the given elements. $\mathrm{Cs} > \mathrm{Al},\ \mathrm{S},\ \mathrm{C}$

Compare $\mathrm{C}$ and $\mathrm{S}$

Although radius decreases across a period, moving down one period increases size significantly. Typical atomic radii show sulfur is slightly larger than carbon. Hence, $\mathrm{C} < \mathrm{S}$

Combine all comparisons

Therefore, the increasing order of atomic radii is $\mathrm{C} < \mathrm{S} < \mathrm{Al} < \mathrm{Cs}$

Match with options

This corresponds to Option C.