An element crystallises in a structure having an fcc unit cell of an edge length 100 pm. If 25 g of the element contains 25 × 1024 atoms, the density of the element is g cm -3.

Question

An element crystallises in a structure having an fcc unit cell of an edge length 100 pm. If 25 g of the element contains 25 × 1024 atoms, the density of the element is g cm -3. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

100 pm =100 × 10-10 cm Volume of unit cell =(100 × 10-10)3 =1 × 10-24 cm 3 Mass of an atom =(25/25 × 1024)=1 × 10-24 g No. of atoms in an fcc unit cell =4 Mass of unit cell =4 × 1 × 10-24 =4 × 10-24 g Density =( text Mass / text Volume ) =(4 × 10-24/1 × 10-24)=4 g cm -3

Q. An element crystallises in a structure having an fcc unit cell of an edge length 100pm. If 25g of the element contains 25×1024 atoms, the density of the element is ____ gcm−3.

100pm=100×10−10cm Volume of unit cell =(100×10−10)3 =1×10−24cm3 Mass of an atom =25×102425​=1×10−24g No. of atoms in an fcc unit cell =4 Mass of unit cell =4×1×10−24 =4×10−24g Density = Volume Mass ​ =1×10−244×10−24​=4gcm−3

Q. An element crystallises in a structure having an $f cc$ unit cell of an edge length $100 p m$ . If $25 g$ of the element contains $25 \times 1 0^{24}$ atoms, the density of the element is ____ $g c m^{- 3}$ .