Question

Nickel (ni) has the fcc crystal structure, an atomic radius of 0.1246 nm, and an atomic weight of 58.69 g/mol. what is its theoretical density?

Answer 1

Note:
We will be calculating the density in units of gm/cm^3
Therefore, our standard units for this problem will be gram and cm

We are given that:
(1) Ni has an FCC structure, this means that: n = 4 
(2) Ni has an atomic weight = 58.69 g/mol
(3) Ni has an atomic radius = 0.1246 nm

Now, the density of Ni can be calculated using the rule in the attached picture.
Examining the parameters in the rule, we will find that:
(1) n = 4
(2) A is the atomic weight of Ni = 58.69 g/mol
(3) Na is Avogadro's number = 6.022 * 10^23
(4) Vc is the number we want to calculate. We can find its value as follows:
     Vc = a^3  
     a = 2R √2 where R is the radius = 0.1246 nm = 0.1256 * 10^-7 cm
     Vc = (2R √2 )^3 = (√2 *2*0.1246*10^-7)^3
     Vc = 4.377 * 10^-23

Now, we have all the parameters to substitute in the equation and get the theoretical density as follows:
theoretical density = [4*58.69] / [4.377 * 10^-23 * 6.022 * 10^23]
theoretical density = 8.9 gm / cm^3

Hope this helps :)