Electron pairing in atoms
The configuration for the free atoms is:


Ba - $\mathrm{[Xe]\ 6s^2}$
Br - $\mathrm{[Ar]\ 3d^{10} 4s^2 4p^5}$
S - $\mathrm{[Ne]\ 3s^2 3p^4}$
Si - $\mathrm{[Ne]\ 3s^2 3p^2}$


Thus:


Barium has no unpaired electrons.
Bromine has one unpaired electron in 4p subshell.
Sulfur has two unpaired electrons in the 3p subshell.
Silicon has two unpaired electrons in the 3p subshell.