The metal = Platinum(Pt)
Further explanation
FCC : Face centered cubic : the unit structures of the unit cell((other than BCC, HCP)
In FCC ⇒ atoms on every corner and side (total 4 atoms)
The length of the face diagonal (b) = 4 times the atomic radius (r)
Formula :
[tex]\tt b=4r[/tex]
[tex]\tt a=r\sqrt{8}[/tex]
[tex]\tt V=16r\sqrt{2}=a^3[/tex]
[tex]\tt \rho=\dfrac{n.Ar}{V.No}[/tex]
Ar = atomic mass, g/mol
No = Avogadro number = 6.02.10²³
n = number of atoms
V = volume (cm³)
a = side length
b = diagonal of the side surface
r = atomic radius
a= 392 pm=3.92 x 10⁻⁸ cm
ρ = 21.45 g/cm³
[tex]\tt V=a^3\\\\V=(3.92\times 10^{-8})^3\\\\V=6.024\times 10^{-23}~cm^3[/tex]
The atomic mass :
[tex]\tt 21.45~g/cm^3=\dfrac{4\times Ar}{6.024\times 10^{-23}\times 6.02\times 10^{23}}\\\\Ar=194.47\approx 195~g/mol[/tex]
radius :
[tex]\tt a=r\sqrt{8}\\\\3.92\times 10^{-8}=r\sqrt{8}\\\\r=1.386\times 10^{-8}~cm[/tex]
Element with atomic mass 195 g/mol and radius = 139 pm (1.386x10⁻⁸cm) = Platinum(Pt)
