The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively

Question

The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively (A) 2√2r, (4r/√3), 2r (B) (4r/√3), 2√2r, 2r (C) 2r, 2√2r, (4r/√3) (D) 2r, (4r/√3), 2√2r

Tardigrade Admin · Accepted Answer

In FCC: The atoms at the face diagonals touch each. If a is the edge length of cube and

r

is the radius of the atom.
So,

2 a = 4 r

< b r / >\Rightarrow a = 22 r < b r / >

In bcc: The atoms at the body diagonal touch each other.
So,

3 a = 4 r

< b r / >\Rightarrow a = \frac{4}{3} r < b r / >

In simple cubic: The atoms at the corners touch each other. So,

a = 2 r

Q. The edge lengths of the unit cells in terms of the radius of spheres constituting $f cc$ , $b cc$ and simple cubic unit cell are respectively

$22 r$ , $\frac{4 r}{3}$ , $2 r$

$\frac{4 r}{3}$ , $22 r$ , $2 r$

$2 r$ , $22 r$ , $\frac{4 r}{3}$

$2 r$ , $\frac{4 r}{3}$ , $22 r$

Q. The edge lengths of the unit cells in terms of the radius of spheres constituting fcc, bcc and simple cubic unit cell are respectively

22​r, 3​4r​, 2r

3​4r​, 22​r, 2r

2r, 22​r, 3​4r​

2r, 3​4r​, 22​r

Q. The edge lengths of the unit cells in terms of the radius of spheres constituting $f cc$ , $b cc$ and simple cubic unit cell are respectively

$22 r$ , $\frac{4 r}{3}$ , $2 r$

$\frac{4 r}{3}$ , $22 r$ , $2 r$

$2 r$ , $22 r$ , $\frac{4 r}{3}$

$2 r$ , $\frac{4 r}{3}$ , $22 r$