Chemistry - Solid State Question with Solution | TestHub

ChemistrySolid StateCubic CrystalsMedium2 minQB

ChemistryMediumsingle choice

Passage / Comprehension

The density of a unit cell is represented as:

$ρ = \frac{E ff ec t i v e n o . o f a t o m ( s ) \times A t o mi c ma ss / f or m u l ama ss}{V o l u m eo f a u ni t ce ll} = \frac{Z \cdot M}{N _{A} \cdot a ^{3}}$

where:

Mass of unit cell = mass of effective no. of atom(s) or ion(s).

$M$ = Atomic mass/formula mass

$N_{A}$ = Avogadro's number $\Rightarrow 6 \times 1 0^{23}$

$a$ = edge length of unit cell

An element crystallizes in a structure having fcc unit cell of an edge 200 pm . Calculate the density, if 100 g of this element contains $12 \times 1 0^{23}$ atoms :

Options:

Answer:

Solution:

Mass of $12 \times 1 0^{23}$ atoms $= 100 gm$ . Mass of $6.022 \times 1 0^{23}$ atoms:

$= \frac{100}{12 \times 1 0 ^{23}} \times 6.022 \times 1 0^{23} = 50.18$

Therefore, the density $ρ$ is:

$ρ = \frac{4 \times 50.18 \times 10}{6.023 \times 1 0 ^{23} \times ( 200 \times 1 0 ^{- 10} ) ^{3}} = 41.66 g / cm^{3}$

Stream:JEESubject:ChemistryTopic:Solid StateSubtopic:Cubic Crystals

⏱ 2mℹ️ Source: QB

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