Question:

An elemental crystal has a density of 8570kg/m38570 \,kg / m ^{3}. The packing efficiency is 0.680.68. The closest distance of approach between neighbouring atom is 2.86?2.86 \,?. What is the mass of one atom approximately?

Updated On: Jan 30, 2025
  • 93 amu
  • 39 amu
  • 63 amu
  • 29 amu
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The Correct Option is A

Solution and Explanation

The packing efficiency =0.68= 0.68, means the given lattice is BCC.
The closest distance of approach =2r= 2r
2r=2.86?=a32r = 2.86\, ? = a \sqrt{3}
or a=2×2.863=3.30?a = \frac{ 2 \times 2.86}{\sqrt{3}} = 3.30\,?
Let atomic weight of the element =a= a
2×936×1023×(3.3)3×1024=8.57\therefore \frac{2 \times9}{36 \times10^{23} \times\left(3.3\right)^{3} \times10^{-24}} = 8.57
a=8.57×3×(3.3)3×0.1a = 8.57 \times 3 \times \left(3.3\right)^{3} \times 0.1
=92.3993 = 92.39 \simeq 93 amu
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