To find the number of atoms in 274.66 g of barium, you need to know the atomic weight of barium and convert the weight to moles. The atomic weight of barium is 137.327 g/mol. Using the formula:
mol = weight/atomic weight
we find that 274.66 g of barium is equivalent to 2.00 mol of barium. Since there are Avogadro's number of atoms per mole, the number of atoms of barium in 274.66 g is equal to 2.00 mol * 6.022 x 10^23 atoms/mol = 1.20 x 10^24 atoms.