A metal crystallises in face centred cubic structure with metallic radius √2A°. The volume of the unit cell (in m3) is

Question

A metal crystallises in face centred cubic structure with metallic radius √2A°. The volume of the unit cell (in m3) is (A) 4 × 10-10 (B) 6.4 × 10-29 (C) 4 × 10-9 (D) 6.4 × 10-30

Tardigrade Admin · Accepted Answer

For FCC, Atomic radius (r)=(√2 a) / 4 ⇒ √2 × 10-10=(√2 a ) / 4 ⇒ a =(4 × √2 × 10-10) / √2=4 × 10-10 m Volume of unit cell = a 3=(4 × 10-10)3 =64 × 10-30 m 3=6.4 × 10-29 m 3

Q. A metal crystallises in face centred cubic structure with metallic radius $2 A^{\circ}$ . The volume of the unit cell (in $m^{3}$ ) is

$4 \times 1 0^{- 10}$

$6.4 \times 1 0^{- 29}$

$4 \times 1 0^{- 9}$

$6.4 \times 1 0^{- 30}$

For FCC,

Atomic radius $(r) = (2 a) /4$

$\Rightarrow 2 \times 1 0^{- 10} = (2 a) /4$

$\Rightarrow a = (4 \times 2 \times 1 0^{- 10}) / 2 = 4 \times 1 0^{- 10} m$

Volume of unit cell $= a^{3} = (4 \times 1 0^{- 10})^{3}$

$= 64 \times 1 0^{- 30} m^{3} = 6.4 \times 1 0^{- 29} m^{3}$

Q. A metal crystallises in face centred cubic structure with metallic radius 2​A∘. The volume of the unit cell (in m3) is

4×10−10

6.4×10−29

4×10−9

6.4×10−30