Ar is a solid below -189 o C with a face-centered cubic array of atoms and a sup

Question

Ar is a solid below -189 oC with a face-centered cubic array of atoms and a supposed density of 1.66 g/cm3. Assuming that the atoms are spheres in contact along the face diagonal, what is the radius of a Ar atom (in Angstroms)? An angstrom = 10-10 m or 10-8 cm. Hint, first find the length of an edge of the unit cell. (Argon's actual density is 1.65 g/cm3.)
Ar is a solid below -189 oC with a face-centered cubic array of atoms and a supposed density of 1.66 g/cm3. Assuming that the atoms are spheres in contact along the face diagonal, what is the radius of a Ar atom (in Angstroms)? An angstrom = 10-10 m or 10-8 cm. Hint, first find the length of an edge of the unit cell. (Argon's actual density is 1.65 g/cm3.)

Explanation / Answer

density=mass/volume

number of atoms in 1 unit cell=4

or density=molar mass*n/(a^3*Na)

or 1650=40*10^-3*4/(a^3*6*10^23)

or a=5.447*10^-10 m

so 4r=2^0.5 *a

so,

4*r=2^0.5 * 5.447*10^-10

or r=1.926*10^-10 m

=1.926 Angstormss

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