Question

A metal can be crystallised in both bcc and fcc unit cells whose edgelengths are 2pm and 4pm respectively.then ratio of densities of fcc and bcc unit cells is​

Answer 1

▶ Solution :

✴ Given :

A metal can be crystallised in both BCC and FCC unit cells whose edge lengths are 2pm and 4pm respectively.

✴ To Find :

Ratio of densities of FCC and BCC unit cells.

✴ Formula :

✏ Formula of density of unit cell in terms of no. of atoms in an unit cell, molecular weight of metal, avegrado's number and edge length of unit cell is given by...

$\boxed{\bf{\pink{d=\dfrac{Z\times M_w}{a^3\times N_A}}}}$

• d denotes density
• Z denotes no. of atoms in an unit cell
• Mw denotes molecular weight of metal
• N$_A$ denotes avegrado's number
• a denotes length of edge

⏭ Z for BCC unit cell = 2

⏭ Z for FCC unit cell = 4

✴ Calculation :

$\rightarrow\bf\:\dfrac{d_1}{d_2}=\dfrac{Z_1\times {a_2}^3}{Z_2\times {a_1}^3}\\ \\ \rightarrow\sf\:\dfrac{d_1}{d_2}=\dfrac{4\times (4)^3}{2\times (2)^3}\\ \\ \rightarrow\sf\:\dfrac{d_1}{d_2}=2\times (2)^3\\ \\ \rightarrow\boxed{\bf{\purple{d_{FCC}:d_{BCC}=16:1}}}$