An element crystallizes into a structure which may be described by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its body diagonals. If the volume of this unitis24 xx 10^(-24)"cm"^(3)and density of element is7.2 g cm ^(-3),calculate the number of atoms present in 200 g of the element.

An element crystallizes into a structure which may be described by a c

1.	An element crystallizes into a structure which may be described by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its body diagonals. If the volume of this unitis24 xx 10^(-24)"cm"^(3)and density of element is7.2 g cm ^(-3),calculate the number of atoms present in 200 g of the element.
Answer» Solution :No. of atoms per unit cell ` = 8 XX 1/8 + 2 = 3 ,i.e. , Z =3 ` Volume of the unit cell = ` a^(3) = 24 xx 10^(-24) " cm" ^(3)` ` p = ( Z xx M)/ ( a^(3) xx N_(0))` ` 7.2 = (3xx M) / (( 24 xx 10^(-24) ) xx ( 6.023 xx 10^(23)) )or M = 34.69` Thus, 34.69g of the element have to atoms =`6.023 xx 10^(23)` 200 G of the element will have atoms ` = ( 6.023 xx 10^(23))/(34.69) xx 200 = 3.4722 xx 10^(24)` atoms