Question

Silver metal crystallises in a cubic closest – packed arrangement with the edge of the unit cell having a length $a = 407pm.$. What is the radius of silver atom.

• A. 143.9 pm
• B. 15.6 pm
• C. 11.59 pm
• D. 13.61 pm

Answer 1

Answer: (A)

143.9 pm

Answer 2

$AC^{2} + AB^{2} = BC^{2}$

here $AC = AB = a,$ $BC = 4r$

$a^{2} + a^{2} = (4r)^{2}$

$2a^{2} = 16r^{2}$

$\therefore$ $r^{2} = \frac{a^{2}}{8}$

$\therefore$ $r = \frac{a}{2\sqrt{2}} = \frac{407}{2\sqrt{2}} = 143.9pm$.