An element has a bcc structure with a celledge of `288` pm. The density of the element is `7.2 g cm^(-3)`. How many atins are present in `208 g` of the element?

Explanation

`"Edge length of the unit cell "=288pm=288xx10^(-10)cm`
Volume of the unit cell `=(288xx10^(-10))^(3)cm^(3)=2.39xx10^(-23)cm^(3)`
Mass of element `=208g`
Density of element `=7.2gcm^(-3)`
`"Volume of 208 g of the element"=("Mass")/("Density")`
`"Mass of an atom"=(208g)/(7.2g cm^(-3))=28.89cm^(3)`
`"Number of unit cells in this volume "=("Volume of element")/("Volume of unit cell")=(28.89cm^(3))/(2.39xx10^(-23)cm^(-3)//" unit cell")`
`=12.08xx10^(23)" unit cell"`
Since the structure is bcc, number of atoms present in a unit cell = 2
The number of atoms in 208 g of the element
`=2xx12.08xx10^(23)=24.16xx10^(23)" atoms"`
`"or "=2.416xx10^(24)" atoms"`