Final answer:
Cesium (Cs) has the greatest atomic radius among the listed elements, as it is located in the lower left side of the periodic table where the atomic size increases.
Step-by-step explanation:
To determine which element has the greatest atomic radius among hydrogen (H), chlorine (Cl), cesium (Cs), and nitrogen (N), we refer to the trends observed in the periodic table. The atomic radius tends to increase as we move down a group and decrease as we move across a period from left to right. Given the choices, cesium (Cs) is located in the lower left side of the periodic table, which indicates that it will have a much larger atomic radius compared to the other elements listed which are higher and/or to the right. Therefore, the element with the greatest atomic radius is cesium (Cs).
When comparing ions, for example, it is known that cations with larger charges are smaller than those with smaller charges. Additionally, as we proceed down the groups of the periodic table, cations of successive elements with the same charge have larger radii, due to the increase in the principal quantum number, n. This provides further justification for cesium's larger atomic size relative to the other elements mentioned.