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)

Explanation

`rho=(ZxxM)/(a^3xxN_0)` or `a^3=(ZxxM)/(rhoxxN_0)=(4xx0.027 kg mol^(-1))/(2700 kg m^(-3) xx6.02xx10^23 mol^(-1))`
`=66.4 xx 10^(-30) m^3 "or" a=(66.4)^(1//3) xx10^(-10) m`
Putting `(66.4)^(1//3) =x, log x=1/3 log 66.4=1.8222/3=0.6074 therefore x=0.4.050 therefore a=4.05xx10^(-10)` m
For fcc, `r=a/(2sqrt2)=(4.05xx10^(-10)m)/(2xx1.414)=1.43xx10^10` m