Question

The density of an unknown metal is 1.55 and its atomic radius is 0.197 . It has a face-centered cubic lattice. What is the atomic weight of this metal?

Answer 1

I could work this problem if it had units. No units on density, none on radius (that could be pm, nm, what?).

Answer 2

Sorry about that - the density is 1.55 g/cm3 and the radius is 0.197 nm.

Answer 3

There are 4 atoms to the unit cell in a fcc.
(4*atomic mass /6.02 x 10^23) = mass of unit cell. You need the mass.

4*radius atom = a*2^1/2
Solve the last equation for a

volume of unit cell = a³

Then plug into mass = volume x density to calculate mass of unit cell. Plug mass into the top equation to calculate atomic mass.

Answer 4

By the way, I would not use the radius in pm. I would change that to cm first thing out of the cage; otherwise you must convert volume in pm³ to cc and that's a little more difficult and one more step to make an error. Same thing for your next post.