Question

Sodium metal crystallises in a body-centred cubic lattice with a unit cell edge of 4.29 Å. The radius of the sodium atom is approximately ______.

Options

• 5.72 Å

• 0.93 Å

• 1.86 Å

• 3.22 Å

Answer 1

Sodium metal crystallises in a body-centred cubic lattice with a unit cell edge of 4.29 Å. The radius of the sodium atom is approximately 1.86 Å.

Explanation:

Edge length (a) = 4.29 Å

In a BCC lattice, atoms touch along the body diagonal. The relationship is

`sqrt 3 * a = 4 r`

`r = (sqrt 3 a)/4`

Substitute a = 4.29 Å

`r = (1.732 xx 4.299)/4`

`r = 7.433/4`

r = 1.86 Å

∴ The radius of the sodium atom is approximately 1.86 Å.