SATHEE: Solid State - Result Question 44

Solid State - Result Question 44

####44. Chromium metal crystallises with a body centred cubic lattice. The length of the unit edge is found to be $287 p m$ . Calculate the atomic radius. What would be the density of chromium in $g / c m^{3}$ ?

(1997, 3M)

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Answer:

Correct Answer: 44. $(7.3 g / c m^{3})$

Solution:

In bcc unit cell, $4 r = \sqrt{3} a$

$\Rightarrow r (C r) = \frac{\sqrt{3} a}{4} = \frac{\sqrt{3}}{4} \times 287 p m = 124.3 p m$

Density of solid $= \frac{N M}{N_{A} \cdot a^{3}}$

$N =$ Number of atoms per unit cell, $M =$ Molar mass

$a^{3} =$ Volume of cubic unit cell, $N_{A} =$ Avogadro’s number

$= \frac{2 \times 52 g}{6.023 \times 10^{23}} \times {(\frac{1}{2.87 \times 10^{- 8} c m})}^{3} = 7.3 g / c m^{3}$

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Solid State - Result Question 44

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