Question:

A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its molar mass is about $50\, g\, mol^{-1}$. What would be the density of the metal (in $g\, cm^{-3}$)?

Updated On: Jul 5, 2022
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The Correct Option is B

Solution and Explanation

$a = 300\, pm,\, Z = 2$ (for bcc unit cell) $M = 50 \,g\,mol^{-1}$ Density, $\rho = \frac{Z\times M}{N_{A} \times a^{3}\times 10^{-30}} g \,cm^{-3}$ $= \frac{2\times 50}{N_{A}\times 10^{23}\times \left(300\right)^{3}\times 10^{-30}} =\frac{100}{6.02\times 27\times 10^{-1}}$ $= \frac{1000}{6.02\times 27} = 6.15\,g\,cm^{-3} \approx 6.2\,g \,cm^{-3}$
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Notes on The solid state

Concepts Used:

Solid State

Solids are substances that are featured by a definite shape, volume, and high density. In the solid-state, the composed particles are arranged in several manners. Solid-state, in simple terms, means "no moving parts." Thus solid-state electronic devices are the ones inclusive of solid components that don’t change their position. Solid is a state of matter where the composed particles are arranged close to each other. The composed particles can be either atoms, molecules, or ions. 

Solid State

Types of Solids:

Based on the nature of the order that is present in the arrangement of their constituent particles solids can be divided into two types;

  • Amorphous solids behave the same as super cool liquids due to the arrangement of constituent particles in short-range order. They are isotropic and have a broad melting point (range is about greater than 5°C).
  • Crystalline solids have a fixed shape and the constituent particles are arranged in a long-range order.