Question

Silver has an atomic radius of $144$ pm and the density of silver is $10.6gc{m}^{-3}$. To which type of cubic crystal silver belongs?

• A. Simple Cubic
• B. BCC
• C. FCC
• D. None of the above

Answer 1

Answer: (C)

FCC

$d=\frac{zM}{N_A\times V}$

$10.6=\frac{z\times 108}{6.023\times {10}^{23}\times (a{)}^3}$

$a^3=\frac{z\times 108}{6.023\times 10.6\times {10}^{23}}$

$a^3=z\times 1.69\times {10}^{-23}$
Now we have to check three cases-

Simple Cubic - $a=2r$ and $z=1$

BCC - $a=\frac{4r}{\sqrt{3}}$ and $z=2$

FCC - $a=2\sqrt{2}r$ and $z=4$

where $r=144$ pm

For this case, FCC satisfies.