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

NTA Abhyas 2020 · Chemistry · Solid State

A crystalline solid of a pure substance has a face-centred cubic...

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm−3cm^{- 3} , then the number of atoms present in 128 g of the crystal is

Options

  1. A2×10242 \times 1{0}^{24}
  2. B4×10244 \times 1{0}^{24}
  3. C1×10241 \times 1{0}^{24}
  4. D3×10243 \times 1{0}^{24}

Correct answer

C. 1×10241 \times 1{0}^{24}

Step-by-step solution

d=Z×Ma3×NA⇒M=a3×d×NAZd = \dfrac{Z \times M}{a^{3} \times {N}_{A}} ⇒ M = \dfrac{a^{3} \times d \times {N}_{A}}{Z}
M=(400)3×10−30×8×NA4M = \dfrac{( 400{)}^{3} \times 1{0}^{- 30} \times 8 \times {N}_{A}}{4}
On solving M=64×2×10−24NAgM = 64 \times 2 \times 1{0}^{- 24}{N}_{A}g
Now, (64×2×10−24NA)\left(64 \times 2 \times 1{0}^{- 24}{N}_{A}\right) g contains NA{N}_{A} atoms
~128gwillcontain=NA64×2×10−24NA×128128gwillcontain = \dfrac{NA}{64 \times 2 \times {10}^{- 24}{N}_{A}} \times 128
=1×1024= 1 \times 1{0}^{24}
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