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Question

Chromium metal crystallises with a body centered cubic lattice. The edge length of the unit cell is found to be 287 pm. Calculate the atomic radius. What would be the density of chromium in g/cm3? (atomic mass of Cr=52.99)

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Solution

For body centred cubic cell atomic radius
r=3×edgelength4=3×2874=124.47pm
Thus, atomic radius of chromium metal is 124.27 pm.
Density of the unit cell of the solid =MassofunitcellVolumeofunitcell
Mass of unit cell = No. of atoms in unit cell (z)× mass of each atom (m)
For body centered cubic lattice, the number of atoms in unit cell (z) is
1+(18×8)=1+1=2
Mass of each atom (m)=AtomicmassAvogadrosno.=52.996.023×1023
The volume of the cubic lattice=(Edgelength)3=(287×1010)3
Density of the unit cell is =2×52.996.023×1023×(287)3×1030gm/cm3
7.44gm/cm3
Thus, the density of chromium is gm/cm3 is 7.44.

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