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mars1129 [50]
2 years ago
15

33.Platinum crystallizes with the face-centered cubic unit cell. The radius of a platinum atom is 139 pm. Calculate the edge len

gth of the unit cell and the density of platinum in g/cm3.
Mathematics
1 answer:
marin [14]2 years ago
6 0

Answer:

The unit cell edge length is 393.21 pm.

The density of platinum is 21.31 g/cm^3

Step-by-step explanation:

Number of atom in FCC unit cell = Z = 4

Density of platinum =

Edge length of cubic unit cell= a= ?

Radius of the platinum atom, r = 139 pm

r = 0.3535 a

a=\frac{139 pm}{0.3535}=393.21 pm=393.21\times 10^{-10} cm

1 pm = 10^{-10} cm

Atomic mass of Pt(M) = 195.08 g/mol

Formula used :  

\rho=\frac{Z\times M}{N_{A}\times a^{3}}

where,

\rho = density

Z = number of atom in unit cell

M = atomic mass

(N_{A}) = Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'.

d=\frac{4\times 195.08 g/mol}{6.022\times 10^{23} mol^{-1}\times (393.21\times 10^{-10} cm)^{3}}

d= 21.31 g/cm^3.

The unit cell edge length is 393.21 pm.

The density of platinum is 21.31 g/cm^3.

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