The correct option is D In 25 g of solid element, the volume occupied by atoms is nearly 2.72 cm3 only
(A) Density of the solid element
d=Z×Ma3×NA
Where,
Z is the number of atoms per unit cell
M is molar mass of the atom
a is the edge length of unit cell
NA is the Avogadro number
Given,
Z for BCC structure = 2
Molar mass = 120 g/mol
Edge length = 400×10−10 cm
d=2×12064×10−24×6×1023
=406.4=10.16 g/cm3=6.25 g/cm3
(B) Number of atoms per unit cell for BCC = 2
Number of unit cell =number of atoms2
Number of atoms =number of moles×NA
Number of moles =massmolar mass
Given mass = 24 g
number of moles =24120=0.2
Number of atoms =0.2×6×1023
Number of unit cell =12×10222
=6×1022
(C) The relationship between radius and edge length for BCC is given by
√3a=4r⇒r=√34×400
=1.732×100 pm=1.732 ∘A
(D) Given mass = 25 g and density = 6.25 g/cm3
Volume of the unit cell =massdensity=256.25
Fraction of the volume occupied by atoms in BCC = 0.68
hence,
Voccupied=0.68×256.25=2.72 cm3