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Question: An element crystallizes in a structure having afcc unit cell of an edge 200 pm. If 200 g of this ele...

An element crystallizes in a structure having afcc unit cell of an edge 200 pm. If 200 g of this element contains 24×102324 \times 10^{23}atoms then its density is

A

41.66gcm−341.66gcm^{- 3}

B

313.9cm−3313.9cm^{- 3}

C

8.117gcm−38.117gcm^{- 3}

D

400gcm−3400gcm^{- 3}

Answer

41.66gcm−341.66gcm^{- 3}

Explanation

Solution

Molar mass of the element

=20024×1023=6.023×1023= \frac{200}{24 \times 10^{23}} = 6.023 \times 10^{23}

=50.19gmol−1= 50.19gmol^{- 1}

For fcc, Z = 4, V=a3=(200×10−10)3V = a^{3} = (200 \times 10^{- 10})^{3}

d=Z×MNA×V=4×50.196.023×1023×(200×10−10)3d = \frac{Z \times M}{N_{A} \times V} = \frac{4 \times 50.19}{6.023 \times 10^{23} \times (200 \times 10^{- 10})^{3}}