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A element X with atomic mass 60 g/mol ha...

A element X with atomic mass 60 g/mol has a density of `6.23"g cm"^(-3)`. If the edge length of the unit cell is 400 pm, identify the type of the cubic unit cell. Calculate the radius of the atoms of the element.

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A = 60 g/mol `" " rho = 6.25 g//cm^(3)`
a = 400 pm or `400xx10^(-10)cm`
`therefore V = a^(3)=(400xx10^(-10))^(3)`
Z = ?
`Z = (rho xx N_(0)xx a^(3))/(M)=(6.25xx6.02xx10^(23)xx(400xx10^(-10))^(3))/(60)`
`therefore` Z = 4. Hence, it is face - centred cubic unit cell.
For fcc, `4r = sqrt(2)a`
`therefore r = (sqrt(2)a)/(4)`
`therefore r = (1.414xx400)/(4)=141.4` pm
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