Final answer:
There are approximately 3.97 x 10^23 atoms of bromine in 52.76 grams of the element, calculated using the average atomic mass and Avogadro's number.
Step-by-step explanation:
To determine the number of atoms in 52.76 grams of bromine, first, we must calculate the number of moles of bromine present in the sample. The average atomic mass of bromine is calculated based on the isotopic masses and abundances of its isotopes, 79Br and 81Br. Using this information, we can establish the weighted atomic mass for bromine:
Average Atomic Mass of Bromine = (0.5069 × 78.9183 amu) + (0.4931 × 80.9163 amu) = 79.904 amu
Next, we convert the mass of bromine to moles:
Number of moles = mass (g) ÷ atomic mass (g/mol)
Number of moles = 52.76 g ÷ 79.904 g/mol = 0.660 moles
To find the number of atoms, we use Avogadro's number (6.022 × 1023 atoms/mol):
Number of atoms = number of moles × Avogadro's number
Number of atoms = 0.660 moles × 6.022 × 1023 atoms/mol = 3.97 × 1023 atoms
Therefore, approximately 3.97 × 1023 atoms of bromine are found in 52.76 grams of bromine.