Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of $4 \AA$. The radius of sodium atom is ____ $\times 10^{-1} \AA$ (Nearest integer)

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Solid State

Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of

4 \overset{˚}{A}

. The radius of sodium atom is ____

\times 1 0^{- 1} \overset{˚}{A}

(Nearest integer)

Answer: 17

For a body-centered cubic (BCC) lattice, the relationship between the edge length a and atomic radius r is:

3 a = 4 r

Given a = 4 Å:

3 \times 4 = 4 r

r = 3 = 1.732 \overset{˚}{A}

Expressing as

x \times 1 0^{- 1}

Å: r = 17.32 × 10⁻¹ Å ≈ 17 × 10⁻¹ Å (nearest integer).

Therefore, x = 17.

JEE Main · 2023 · 13 Apr 2023 · Shift 2 · Integer answer