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

NTA Abhyas 2020 · Chemistry · Solid State

How many unit cells are present in a cube shaped ideal crystal of...

How many unit cells are present in a cube shaped ideal crystal of NaCl\text{NaCl} of mass 1.00g1.00 g?

Options

  1. A2.57×10212.57 \times {10}^{21}
  2. B5.14×10215.14 \times {10}^{21}
  3. C1.28×10211.28 \times {10}^{21}
  4. D1.71×10211.71 \times {10}^{21}

Correct answer

A. 2.57×10212.57 \times {10}^{21}

Step-by-step solution

∴ \text{Mass}\text{of}\text{one}\text{unit}\text{cell}\text{=}\text{V}\text{\times}\text{d}\text{(V}\text{is}\text{volume,}\text{disdensity)}<br/><br />= a^{3} \times d<br/>Also,density=n×at.wt.a3×av.no.<br />Also, density = \dfrac{n \times at. wt.}{a^{3} \times av. \text{no.}}
∴Massofoneunitcell=a3\timesn\timesat.wt.a3\timesav.no.=n\timesat.wt.av.no.∴ \text{Mass}\text{of}\text{one}\text{unit}\text{cell}\text{=}\dfrac{a^{3} \text{\times}\text{n}\text{\times}\text{at}\text{.wt}\text{.}}{a^{3} \text{\times}\text{av}\text{.no}\text{.}} \text{=}\dfrac{\text{n}\text{\times}\text{at}\text{.wt}\text{.}}{\text{av}\text{.no}\text{.}}
\text{=}\dfrac{\text{4 \times 58}\text{.5}}{\text{6}{\text{.02 \times 10}^{\text{23}}} \text{(n}\text{=}\text{4}\text{for}\text{cubic}\text{shape)}
=38.87×10−23g= 38.87 \times {10}^{- 23}g
\text{No}\text{.}\text{of}\text{unit}\text{cell}\text{in}\text{1}\text{g}\text{=}\dfrac{1}{\text{38}\text{.87}\text{\times}{\text{10}^{\text{23}}} \text{=}\text{2}\text{.57}\text{\times}{\text{10}^{\text{21}}
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