Question

A certain element crystallises in a bcc lattice of unit cell edge length 27 A°. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in A° will be ______. (Round off to the Nearest Integer).

[Assume each lattice point has a single atom]

Options

• 31

• 32

• 33

• 34

Answer 1

A certain element crystallises in a bcc lattice of unit cell edge length 27 A°. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in A° will be 33.

Explanation:

For bcc unit cell, `sqrt3"a"` = 4R

a = `(4"R")/sqrt3`

27 = `(4"R")/sqrt3`

R = `27sqrt3/4`

For fcc unit cell, `sqrt2"a"` = 4R

a = `4/sqrt2(27sqrt3/4)`

a = `27sqrt3/sqrt2`

a = 33.12 ≈ 33