To find the molar mass (Ar) of a compound, we first need to find the number of moles of each element present in the compound using the given masses and molar masses.

Given:
Mass of bromine (Br) = 0.512 g
Mass of bromine dioxide (Br2O) = 0.64 g

First, let's find the number of moles of bromine (Br):
Molar mass of bromine (Br) = 79.904 g/mol
Number of moles of Br = Mass / Molar mass
Number of moles of Br = 0.512 g / 79.904 g/mol ≈ 0.0064 mol

Next, let's find the number of moles of bromine dioxide (Br2O):
Molar mass of bromine dioxide (Br2O) = 159.808 g/mol
Number of moles of Br2O = Mass / Molar mass
Number of moles of Br2O = 0.64 g / 159.808 g/mol ≈ 0.004 mol

Since the formula of bromine dioxide is Br2O, and we found that there are 0.0064 moles of bromine and 0.004 moles of bromine dioxide, we can determine the atomic mass of Br as follows:

Ar(Br) = (0.512 g * 1 mol/79.904 g) / 0.0064 mol = 8 g/mol

Therefore, the atomic mass of bromine (Br) is 80 g/mol.