1.

An element crystallises in fcc lattice with cell edge of 400 pm. Calculate its density if 250 g of this element contain `2.5 xx 10^(24)` atoms.

Answer» Z = 4
`a = 400 "pm" = 400 xx 10^(-10) cm`
`6.022 xx 10^(23)` atoms has a mass = molecular mass (M)
`2.5 xx 10^(24)` atoms has mass = 250 g
`6.022 xx 10^(23)` atoms has mass = `(250)/(2.5 xx 10^(24)) xx 6.022 xx 10^(23)`
Molecular mass (M) = 60.22g
`d=(Z xx M)/((a)^(3)xxNa)`
`d = (4 xx cancel60.22)/((400xx10^(-10))^(3)xxcancel(6.022)xx10^(23))`
`d = (cancel(400))/(cancel(4)xx4xx4) = d = (10)/(16) = 6.25 g//cm^(3)`


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