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

NTA Abhyas 2020 · Chemistry · Solid State

X = 5Å Y = 8Å Molar mass of solid = 259.8g mo ^ - 1 A solid...

X = 5Å Y = 8Å Molar mass of solid = 259.8g mo ^ - 1 A solid crystallises in hexagonal lattice as shown in above figure.

X=5A˚X = 5Å
Y=8A˚Y = 8Å
Molar mass of solid = 259.8\text{g mo}{\textl^{- 1}

A solid crystallises in hexagonal lattice as shown in above figure. Density of the solid is 5 g/ml\text{5 g/ml}. How many molecules are their in the given unit cell?
(Avagadro's number =6.023×1023= 6.023 \times 1{0}^{23} )

Options

  1. A2
  2. B3
  3. C4
  4. D6

Correct answer

A. 2

Step-by-step solution

Volume of unit cell = Area of base ×\times height

=X2sin⁡60°×Y= X^{2}\sin 60 ° \times Y

=(5×10−8)2×0.866×8×10−8= {\left(5 \times 1{0}^{- 8}\right)}^{2} \times 0.866 \times 8 \times 1{0}^{- 8}

=1.732×10−22cm3= 1.732 \times 1{0}^{- 22}cm^{3}

Number of molecules in the unit cell =Volume×DensityMolarmass×6.023×1023= \dfrac{Volume \times Density}{Molar\text{mass}} \times 6.023 \times 1{0}^{23}

=1.732×10−22×5259.8×6.023×1023≈2= \dfrac{1.732 \times 1{0}^{- 22} \times 5}{259.8} \times 6.023 \times 1{0}^{23} \approx 2.
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