1. Rubidium metal has a body-centered cubic structure. The density of the metal
ID: 883955 • Letter: 1
Question
1. Rubidium metal has a body-centered cubic structure. The density of the metal is 1.532 g/cm3. Calculate the radius of the rubidium atom. Assume that rubidium atoms are spheres. Then note that each corner sphere of the unit cell touches the body-centered sphere.
2. Copper metal has a face-centered cubic structure. The density of the metal is 8.93 g/cm3. Calculate the radius of the copper atom. Assume that copper atoms are spheres. Then note that the spheres on any face of a unit cell touch along the diagonal.
Explanation / Answer
1)
density of rubidium metal = 1.532 g / cm^3
in bcc structure number of atoms = 2
molecular mass of Rb = 85.46 g/mol
mass of Rb in grams = 85.46 / 6.023 x 10^23
= 1.42 x 10^-22 g
there are 2 atoms in bcc so = 1.42 x 10^-22 x 2
= 2.84 x 10^-22 g
mass of 2 atoms = 2.84 x 10^-22 g
volume of metal = mass / density
= 2.84 x 10^-22 / 1.532
= 1.85 x 10^-22 cm^3
volume = a^3
a = (volume)^1/3
= 5.7 x 10^-8 cm
find radius r
r = sqrt(3) a / 4
= sqrt(3) x 5.7 x 10^-8 / 4
= 2.47 x 10^-8 cm
radius = 2.47 x 10^-8 cm
2)
density of Cu metal = 8.93 g / cm^3
molecular mass of Cu = 63.546 g/mol
mass of Rb in grams = 63.546 / 6.023 x 10^23
= 1.055 x 10^-22 g
there are 4 atoms in fcc so = 1.055 x 10^-22 x 4
= 4.22 x 10^-22 g
mass of 4 atoms = 4.22 x 10^-22 g
volume of metal = mass / density
= 4.22 x 10^-22 / 8.93
= 4.73 x 10^-23 cm^3
volume = a^3
a = (volume)^1/3
= (4.73 x 10^-23)^1/3
= 3.615 x 10^-8 cm
find radius r
4r = sqrt(2) a
4r = sqrt(2) x 3.615 x 10^-8
r = 1.278 x 10^-8 cm
radius = 1.278 x 10^-8 cm
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