We are going to need to calculate the density assuming both structure types. We then compare the densities to the given values to know the appropriate structure.
Before anything else, convert the radius pm to cm to be consistent with the units in the density.
The radius of gold is 144 pm, and the density is 19.32 g/cm3. Does elemental gold have a face-centered cubic structure or a body-centered cubic structure?
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Our data indicates that this problem or a close variation was asked in Chemistry: An Atoms First Approach - Zumdahl Atoms 1st 2nd Edition. You can also practice Chemistry: An Atoms First Approach - Zumdahl Atoms 1st 2nd Edition practice problems.