Question

If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10^-8 cm the radius of metal atom is ______.

Options

• 3.2 × 10^-7 cm

• 1.86 × 10^-8 cm

• 1.07 × 10^-7 cm

• 1.07 × 10^-8 cm

Answer 1

If a metal crystallises in bcc structure with edge length of unit cell 4.29 × 10^-8 cm the radius of metal atom is 1.86 × 10^-8 cm.

Explanation:

The relation between edge length and radius of an atom in a bcc structure is related as:

r = `sqrt3//4"a"`

Given, a = 4.29 × 10^-8 cm

For bcc structure,

r = `sqrt3/4 "a" = sqrt3/4 xx 4.29 xx 10^-8 "cm"`

`= 1.857 xx 10^-8 "cm"`

= 1.86 × 10^-8 cm