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The density of aluminium is ` 2700 " kg m^(-3) ` , Aluminium crytallises in face - centred cubic lattic. Calculate the radius of aluminium atom in meters (Atomic mass of Al = 27)

Answer» ` p = ( Z xx M)/( a^(3) xx N_(0)) or a^(3)= (Z xx M)/(p xx N_(0)) = ( 4 xx 0.027kg mol^(-1))/ (2700 "kg m"^(-3)xx 6.02 xx 10^(23) " mol" ^(-1))`
`= 66.4 xx 10^(-30) m^(3) or a = ( 66.4)^(1//3) xx 10^(-10) m`
Putting `(66.4)^(1//3) = x , log x = 1/3 log 66.4 = (1.8222)/3 = 0.6074 therefore x = 4.050 , therefore a = 4.05 xx 10^(-10)` m
for fcc , ` r = a/(2sqrt2) = (4.05 xx 10^(-10)m)/ ( 2xx 1.414) = 1.43 xx 10^(10) m `


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