Step 1: Understanding the Concept:
In \(\text{BrF}_3\) the central atom is bromine. It has 7 valence electrons (group 17). Three of them pair with fluorine atoms to form three Br-F bonds.
Step 2: Key Formula or Approach:
Bond pairs = number of atoms bonded to the central atom = 3.
Lone pairs = \(\frac{7 - 3}{2} = 2\).
Step 3: Detailed Explanation:
Bromine uses 3 of its 7 electrons for bonding, leaving 4 electrons, which form 2 lone pairs.
So the valence shell has 3 bond pairs and 2 lone pairs, five electron pairs in total. The shape is T-shaped (trigonal bipyramidal arrangement with the two lone pairs in equatorial positions).
Options with only 1 lone pair, or with only 2 bond pairs, do not match three Br-F bonds and seven valence electrons.
Final Answer:
Central bromine carries 2 lone pairs and 3 bond pairs, option (C).
\[ \boxed{2\text{ lone pairs and } 3\text{ bond pairs}} \]