An element occurs in two crystalline form `alpha` and `beta`. The `alpha`-from has an `fcc` with `alpha = 3.68 Å` and `beta`-from has a `bcc` with `a = 2.92 Å`. Calculate the ratio of their densities.

Options

A. 1 . 1
B. `1:2`
C. `2:1`
D. `2:3`

Answer

A

Explanation

`Z_("eff")` for fcc = 4, `Z_("eff")` for bcc = 2
Atomic volume of `alpha-` form `=((3.68xx10^(-8))^(3)xxN_(A))/(4)`
Atomic volume of `beta-` form `=((2.92xx10^(-8))^(3)xxN_(A))/(2)`
(As Atomic mass is sme ,element is same), so the density ratio is
`p_(alpha):p_(beta)=V_(beta):V_(alpha)=((2.92)^(3))/(2):((3.68)^(3))/(4)`
`=12.448:12.459=1:1`