Question

A metal crystallizes in bcc unit cell. The atomic mass of the metal is 55.8 g mol1
, density = 7.9 g cm3
. Calculate the edge length of the unit cell?

Answer 1

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Explanation:

Answer 2

Answer:

The edge length of the unit cell is equal to 2.867×10⁻⁴cm.

Explanation:

We have given,

The atomic mass of the metal = 55.8 g/mol

The density of the unit cell = 7.9 gcm⁻³

The metal is crystallized in BCC unit cell.

So, the number of atoms in BCC unit cell, Z =2

We know the formula of density:

$d=\frac{Z*M}{N_{A}*a^3}$                                                                                ..................(1)

where $N_{A}$ is Avogadro number.

and, 'a' is the edge length of BCC unit cell.

$a^3=\frac{Z*M}{N_{A}*d}$

Substitute the value of Z, M, Avogadro number and density in equation (1);

$a^3=\frac{(2)*(55.8)}{7.9*6.023*10^{23}}$

$a^3=23.45*10^{-24}$

$a= 2.867*10^{-8}cm$

Therefore, the edge length of body centered cubic (BCC) unit cell is equal to  2.867×10⁻⁴cm.