Question

copper crystalliiscs into a bcc structure. density of unit cell is 8.5 g/mol. calculate age length and radius of electron if atomic mass is 63.1 g cm3

Answer 1

The density of metal is given asd=z×Ma3×NAd=z×Ma3×NAFor Simple cubic ,z=1z=1 and a=2ra=2rFor BCC,z=2z=2 and a=43–√a=43rrFor FCC,z=4z=4 and a=42–√a=42rrSubstituting values of z and a in density formula and calculating density ;Given that ,Mass , M=63.54g/molM=63.54g/molRadius, r=127.7×10−10cmr=127.7×10−10cmAvagadro's number NA=6.02×1023NA=6.02×1023For simple cubic ,d=1×63.54(2×127.8×10−10)×6.02×1023d=1×63.54(2×127.8×10−10)×6.02×1023d=6.31gcm−3d=6.31gcm−3For BCC,d=2×63.54(4/3–√×127.8×10−10)3×6.02×1022d=2×63.54(4/3×127.8×10−10)3×6.02×1022d=8.2g.cm−3d=8.2g.cm−3For FCC,d=4×63.54(4/2–√×127.8×10−10)2×6.02×1023d=4×63.54(4/2×127.8×10−10)2×6.02×1023d=8.92g.cm−3d=8.92g.cm−3Given the density =8.95g.cm−3=8.95g.cm−3, which is nearest for FCC.Hence Copper unit cell is face centered cubic.