You're asking about the relative sizes of oxygen and nitrogen atoms, not about the size of the oxygen atom in a water molecule compared to the nitrogen atom. Here's why oxygen is bigger than nitrogen:

* Atomic Number and Electron Configuration: Oxygen has an atomic number of 8, while nitrogen has an atomic number of 7. This means oxygen has one more proton and one more electron than nitrogen. Both elements have the same number of electron shells, but oxygen has one more electron in its outermost shell.

* Electron-Electron Repulsion: The additional electron in oxygen's outer shell experiences more repulsion from the other electrons in that shell. This increased repulsion pushes the electrons further apart, increasing the atom's overall size.

* Effective Nuclear Charge: While oxygen has a larger nucleus with one more proton, the increased number of electrons also provides more shielding from the nucleus's positive charge. This "effective nuclear charge" experienced by the outermost electrons is slightly lower in oxygen, leading to a larger atomic radius.

In summary: Oxygen's larger atomic radius is due to a combination of increased electron-electron repulsion and a slightly lower effective nuclear charge compared to nitrogen.