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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

An elemental crystal has a density of 8570kg / m ^ 3 . The packing...

An elemental crystal has a density of 8570kg/m38570kg / {m}^{3}. The packing efficiency is 0.68. The closest distance of approach between neighbouring atom is 2.86A˚2.86Å. What is the mass in amu of one atom approximately?
[Report your answer by rounding it upto nearset whole number]

Correct answer

93

Step-by-step solution

The packingefficiency=0.68packingefficiency = 0.68, means the given lattice is BCCBCC.

The closest distance of approach=2rapproach = 2r

2r=2.86Ao=3a2⇒2×2.863=3.30Ao2\text{r} = 2.86\overset{o}{\text{A}} = \dfrac{\sqrt{3} \text{a}}{2} ⇒ \dfrac{2 \times 2.86}{\sqrt{3}} = 3.30\overset{o}{\text{A}} .

Let, at. wt. of the element=welement = w

∴2×w6×1023×(3.3)3×10–30=8570∴ \dfrac{2 \times w}{6 \times 1{0}^{23} \times {\left(3.3\right)}^{3} \times 1{0}^{– 30}} = 8570

w=92.39≃93w = 92.39 ≃ 93 amu
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