What is the molecular geometry of BrF_{4}^{-} ? (A) square planar (B) square pyramidal (C) seesaw (D) tetrahedral

To determine the molecular geometry of \( \text{BrF}_4^- \) (bromine tetrafluoride ion), follow these steps:

1. **Determine the number of valence electrons:**
- Bromine (Br) has 7 valence electrons.
- Each fluorine (F) has 7 valence electrons. Since there are 4 fluorine atoms, that’s \( 4 \times 7 = 28 \) electrons.
- The ion has a -1 charge, which adds 1 more electron.

Total valence electrons = 7 (Br) + 28 (F) + 1 (charge) = 36 electrons.

2. **Determine the central atom and its bonding:**
- Bromine is the central atom.
- To determine the number of bonding pairs and lone pairs, start by drawing the Lewis structure. Bromine will be surrounded by four fluorine atoms, with each fluorine forming a single bond with bromine.

3. **Construct the Lewis structure:**
- Bromine forms single bonds with each of the four fluorine atoms. This uses up 8 electrons (4 bonds × 2 electrons per bond).
- After placing the bonding pairs, the remaining electrons are used to complete the octet of fluorine atoms. Each fluorine will have 6 remaining electrons, totaling \( 4 \times 6 = 24 \) electrons.
- We have used 8 electrons for bonding and 24 electrons for lone pairs, totaling 32 electrons, and the total number of valence electrons was 36, so there are 4 electrons left, which will be used as lone pairs on the bromine atom.

4. **Determine the molecular geometry:**
- Bromine in \( \text{BrF}_4^- \) has 4 single bonds and 2 lone pairs of electrons around it.
- To minimize repulsion, the lone pairs and bonding pairs arrange themselves in a way that gives the best spatial arrangement.

In this case:
- The geometry around bromine is influenced by both bonding pairs and lone pairs.
- With 4 bonding pairs and 2 lone pairs, the arrangement will be square planar. This is because the lone pairs occupy opposite sides of the bromine atom, leading to a square planar arrangement for the bonding pairs.

**Answer: (A) square planar**