Final answer:
The elements Ba, S, N, and Li, when arranged in order of increasing atomic radius based on their periodic trends, are N < S < Li < Ba.
Step-by-step explanation:
To arrange the elements Ba, S, N, and Li in order of increasing atomic radius, we need to know the trends of atomic radii in the periodic table. Generally, atomic radius decreases across a period from left to right and increases down a group from top to bottom. Nitrogen (N) is the smallest as it is on the right side of Period 2, sulfur (S) is larger than nitrogen as it is to the left of nitrogen but still in the same period. Lithium (Li), being the first member of its group and placed leftmost on Period 2, is larger than sulfur. Barium (Ba) has the largest radius as it is located at the bottom of Group 2, far below lithium.
Therefore, in increasing atomic radius, the elements are arranged as: N < S < Li < Ba.