Question

If $fcc$ unit cell is converted in to End centred unit cell, then its packing efficiency will decrease by:

• A. $25\%$
• B. $50\%$
• C. $40\%$
• D. $60\%$

Answer 1

Answer: (B)

$50\%$

$Z=4$ for FCC unit cell

In end centered unit cell, $8$ atoms at body corners, $2$ atoms at any $2$ of the face centres.

$Z_{eff}$ for end centred unit cell $=\frac{1}{8}\times 8+2\times \frac{1}{2}=2$

As $packagingfraction\propto Z_{effective}$

$\%$ decrease in packaging fraction $=\frac{4-2}{4}\times 100=50\%$