Density of solid metal in gm/cc is - | TestHub

Passage / Comprehension

A hypothetical metal M (Atomic weight = 450) crystallizes as a cubic crystal such that metal atoms touch each other along the body diagonal of the cube. The edge length of the cubic unit cell is $1 nm$ .

If this metal is melted, its density in molten form is $1.2 g m / cc$ . ( $N_{A} = 6 \times 1 0^{23}$ )

Density of solid metal in gm/cc is -

Options:

Answer:

Solution:

Question Explanation:

Calculate solid metal density based on body diagonal contact.

Concept: BCC Unit Cell Density.

Solution:

Atoms touching along the body diagonal in a cubic crystal indicates a BCC lattice ( $Z = 2$ ). Use the provided edge length and atomic weight to find the density of the solid state.

Calculation:

$Z = 2, M = 450, a = 1 nm = 1 0^{- 7} cm$ .

Density $= \frac{Z \times M}{N _{A} \times a ^{3}} = \frac{2 \times 450}{6 \times 1 0 ^{23} \times ( 1 0 ^{- 7} ) ^{3}} = \frac{900}{600} = 1.5 g / cc$ .

Final Answer: Option (c)

Chemistry - Solid State Question with Solution | TestHub

Options:

Doubts & Discussion