Oxides of nitrogen have open chain structures while those of phosphorous have closed chain or cage structures. Why ?

Explanation

Nitrogen due to its small size and high electronegativity has a strong tendency to form `p pi-p pi` bonds with oxygen and form oxides with open chain structures.
On the other hand, phosphorous due to its large size has no tendency to form `p pi-p pi` bonds with oxygen and prefers to form single bonds. Consequently, a cage-like structure is formed, e.g., in `P_4 O_6`.