The number of atoms in 2.4 g of body centred cubic crystal with length 200 pm is (density=10 g `cm^(-3)` ,NA =`6xx10^(22)` atoms/mol)

Options

A. `6 xx 10^(22)`
B. `6 xx 10^(20)`
C. `6 xx 10^(23)`
D. `6 xx 10^(19)`

Answer

A

Explanation

(a): Density, `rho` = 10 g `cm^(-3)`,
`N_(A) = 6 xx 10^(23)` atoms/mol, a= 200 pm, For bcc, Z=2
`rho = (ZxxM)/(a^(3)xxN_(a))`
10 g `cm^(-3) = (2xxM)/((200xx10^(10)cm)^(3)xx(6xx10^(23)mol^(-1)))`
M = 24 g `mol^(-1)`
24 g of element contains = `6xx10^(23)` atoms
`:.` 2.4 g of element contains = `(6xx10^(23))/(24) xx 2.4` atoms
`= 6xx10^(22)` atoms