Answer:
a)The total number of platinum atoms are [tex]6.620\times 10^{22} atoms[/tex].
b)The radius of a Pt atom is 138.7 pm.
Explanation:
a) Let the total number of platinum atoms be x
And mass of x atoms of platinum be m
Edge length of platinum cube ,s= 1.0 cm
Volume of the cube = [tex]1.0 cm^3[/tex]
Density of the platinum cube = [tex]d=21.45 g/cm^3[/tex]
Mass = Density × Volume
[tex](m)=21.45 g/cm^3\times 1.0 cm^3=21.45 g[/tex]
Mass of an atom of platinum = [tex]3.240\times 10^{-22} g[/tex]
[tex]x\times 3.240\times 10^{-22} g=21.45 g[/tex]
[tex]x=6.620\times 10^{22} atoms[/tex]
b) If only 74 percent of the space inside the cube is taken up by Pt atoms.
Volume occupied by platinum atoms = 74% of [tex]1.0 cm^3[/tex]
[tex]V'= 0.74 cm^3[/tex]
Volume occupied by [tex]6.620\times 10^{22}[/tex] atoms is[tex]0.74 cm^3[/tex].
[tex]6.620\times 10^{22} \times \frac{4}{3}\pi r^3=V'[/tex]
[tex]6.620\times 10^{22} \times \frac{4}{3}\times 3.14\times r^3=0.74 cm^3[/tex]
[tex]r = 1.387\times 10^{-8} m = 138.7 pm[/tex]
The radius of a Pt atom is 138.7 pm.
