Solid State Question 81
Question: A metallic element has a cubic lattice. Each edge of the unit cell is $ 2A^{0} $ . The density of the metal is $ 2gc{{m}^{-3}} $ . The unit cells in 200 g of the metal are
Options:
A) $ 1\times 10^{25} $
B) $ 1\times 10^{24} $
C) $ 1\times 10^{22} $
D) $ 1\times 10^{20} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Edge length of the unit cell $ =2A^{0}=2\times {{10}^{-8}}cm $
Volume of the unit cell $ ={{(2\times {{10}^{-8}})}^{3}}cm^{3} $ $ =8\times {{10}^{-24}}cm^{3} $
Mass of unit cell $ \text{= volume }\times\text{ density} $ $ =8\times {{10}^{-24}}\times 2.5g $
No. of unit cells in 200 g of the metal $ \frac{\text{mass of metal}}{\text{mass of unitcell}}=\frac{200}{8\times {{10}^{-24}}\times 2.5}=1\times 10^{25} $
BETA
