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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 1.00g\text{1}\text{.00}\text{g}?

Options

  1. A2.57×10212 \text{.} 5 7 \times 1 {0}^{2 1}
  2. B5.14×10215 \text{.} 1 4 × 1 {0}^{2 1}
  3. C1.28×10211 \text{.} 2 8 × 1 {0}^{2 1}
  4. D1.71×10211 \text{.} 7 1 × 1 {0}^{2 1}

Correct answer

A. 2.57×10212 \text{.} 5 7 \times 1 {0}^{2 1}

Step-by-step solution

∴∴ Mass of one unit cell =V×d= \text{V} \times \text{d} (V is volume, d is density)

=a3×d= a^{3} \times \text{d}

& Also, density =z×at. wt.a3×av. no.= \dfrac{\text{z} \times \text{at. wt.}}{a^{3} \times \text{av. no.}}

∴∴ Mass of one unit cell=a3×z×at. wt.a3×av. no.= \dfrac{a^{3} \times \text{z} \times \text{at. wt.}}{a^{3} \times \text{av. no.}}

=z×at. wt.av. no.= \dfrac{\text{z} \times \text{at. wt.}}{\text{av. no.}}

=4×58.56.02×1023= \dfrac{4 \times 5 8 \text{.} 5}{6 \text{.} 0 2 \times 1 {0}^{2 3}} (z = 4 for cubic shape)

=38.87×10−23g= 3 8 \text{.} 8 7 \times 1 {0}^{- 2 3} \text{g}

∴∴ No. of unit cell in 1 g =138.87×10−23= \dfrac{1}{3 8 \text{.} 8 7 \times 1 {0}^{- 2 3}}

=2.57×1021= 2 \text{.} 5 7 \times 1 {0}^{2 1}
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