Why is ammonia written as NH4 and not H4N?

Answer 1

The first thing is that your question is flawed. Ammonia is NH3, not NH4. NH4 is ammonium, which takes on an extra Hydrogen atom. That said, the Ammonium atom can certainly be written as H4N as well as the ore common NH4.

Answer 2

Ammonia is written as NH3 and not H4N because nitrogen usually forms three covalent bonds with other atoms, such as in ammonia where it bonds with three hydrogen atoms. The nitrogen atom is located in the center of the molecule, making it more common to write it as NH3 instead of H3N to reflect its bonding pattern.