The chemical formula for two bromine atoms, one nitrogen atom, and one chlorine atom is Br₂NCl.

Here's why:

* Br₂: The subscript "2" indicates there are two bromine atoms.

* N: Represents one nitrogen atom.

* Cl: Represents one chlorine atom.

It's important to note that this molecule is likely unstable and may not exist in a stable form. This is because the electronegativity difference between the elements is quite large, making the molecule highly reactive.