A metal (M=63.5 g mol^-1) with atomic radius 128 pm crystallises in a fcc lattice. Take sqrt2=1.414, N_A=6.022x10^23 mol^-1. Which statements are correct?

The edge length is about 362 pm.

The density is about 8.89 g cm^-3.

The largest sphere fitting an octahedral void has radius about 53 pm.

The edge length is about 362 pm.

The density is about 8.89 g cm^-3.

The nearest-neighbour distance equals the edge length, 362 pm.

The largest sphere fitting an octahedral void has radius about 53 pm.

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ss044

A metal ( $M = 63.5 g mo l^{- 1}$ ) with atomic radius $128 pm$ crystallises in a fcc lattice. Take $2 = 1.414$ , $N_{A} = 6.022 \times 1 0^{23} mo l^{- 1}$ . Which statements are correct?

a = 22 r = 2 \times 1.414 \times 128 = 362.0 pm

ρ = \frac{4 \times 63.5}{6.022 \times 1 0 ^{23} \times ( 3.620 \times 1 0 ^{- 8} ) ^{3}} = 8.89 g c m^{- 3}

. The nearest-neighbour distance is

2 r = 256

pm, not

a

. Octahedral void radius

= 0.414 \times 128 = 53

pm.