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Niobium crystallizes in body-centred cub...

Niobium crystallizes in body-centred cubic structure. If the density is `8.55 g cm^(-3)`, calculate the atomic radius of niobium using its atomic mass `93 u`.

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The following equations link density (D), number of atoms per unit cell (Z), atomic mass (M), Avogadro's number `(N_0)`, and edge length (a):
`"D"=frac{"ZM"}{"N"_0"a"^3}`
Given `"D"=8.55"g"//"cm"^3` and `"M"=93u.`
Edge length`=a=(frac{"ZM"}{"DN"_0}^1//3)=(2xx93//8.55xx6.23xx10^23)^1//3=3.306xx10^-8"cm"`
Atomic radius`=r=frac{sqrt 3}{4}a=frac{sqrt 3}{4}xx3.306xx10^-8=1.432xx10^-8"cm"=14.32"nm"`.
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