Sodium metal crystallizes in body centred cubic lattice with edge length of 4.29 mathringA. The radius of sodium atom is

Question

Sodium metal crystallizes in body centred cubic lattice with edge length of 4.29 mathringA. The radius of sodium atom is (A) 2.857 mathringA (B) 1.601 mathringA (C) 2.145 mathringA (D) 1.857 mathringA

Tardigrade Admin · Accepted Answer

In body centred cubic unit cell (bcc) (sphere along the body diagonal ) r=(√3/4) a where, r= radius of sphere a= edge length a=4.29 mathringA ⇒ r=(√3/4) × 4.29 =1.857 mathringA

Q. Sodium metal crystallizes in body centred cubic lattice with edge length of $4.29 \overset{˚}{A}$ . The radius of sodium atom is

$2.857 \overset{˚}{A}$

$1.601 \overset{˚}{A}$

$2.145 \overset{˚}{A}$

$1.857 \overset{˚}{A}$

In body centred cubic unit cell (bcc) (sphere along the body diagonal )

$r = \frac{3}{4} a$

where, $r =$ radius of sphere

a= edge length

$a = 4.29 \overset{˚}{A}$

$\Rightarrow r = \frac{3}{4} \times 4.29$

$= 1.857 \overset{˚}{A}$

Q. Sodium metal crystallizes in body centred cubic lattice with edge length of 4.29A˚. The radius of sodium atom is

2.857A˚

1.601A˚

2.145A˚

1.857A˚