A given metal crystallises out with a cubic structure having edge length of `361 "pm"` .If there are metal atoms in one cell, what is the radius of one atoms?

Options

A. Density of the structure II is lower than structure I.
B. Density of the structure II is higher than structure I.
C. The pore volume in structure I is 1.2 times higher than that of structure II .
D. The pore volume of both the structures are equal .

Answer

A

Explanation

Structure I , a(I) = `2sqrt(2)r` represent fcc structure
Structure II, a(II) = `(4r)/(sqrt3)` represents bcc structre
Density (I) `= (Zxx M)/(N_A xx a^3) = (4 xx M)/(N_A xx (2sqrt(2)r)^(3))`
Desity (II) = `(Z xxM)/(N_A xx a^3) = (2 xx M)/(N_A xx (((4r)/(sqrt3))^(3)))`
`("Density" (I))/("Density"(II)) = 4/((2sqrt(2)r)^(3)) = (((4r)/(sqrt3))^(3))/2`
`= (4)/(16 xx 1.414 r^3) xx (64 r^3)/(3 xx 2 xx 1.732)`
`= 1.09`
Density (I) = 1.09 Density (II)
Thus, density of structure (II) is lower than that of structure (I). Empty space of bcc is 32% and empty space of fcc is 26%.