1.

N_A spheres of radius 'R' are melted in x xxN_A smaller spheres, so that when fcc lattice is generated from smaller spheres the edge length is formed to be 2 5/6 R.Find x.

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SOLUTION :`N_A xx 4/3 piR^3=x xxN_Axx4/3 pi R^3 implies r=R/ROOT(3)(x)`
In fcc
`sqrt2a=4r. " " implies " " sqrt2xx2^(5//6)R=(4R)/root(3)(x)`
`2^(5/6+1/2)=2^2/x^(1//3)implies x^(1//3)=2^(2 4/3)implies x^(1//3)=2^(2//3) implies x=4`


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