Question

NaCl is a “face-centered” ionic crystal with a unit cell side length of 564 pm. Find the volume in cm3 of the
empty space inside one NaCl unit cell (aka. interstitial sites)

Answer 1

face centred means 1/2 part of phere in each face and cube has 6 faces so total sphere is 3.and 1/8 part of each sphere at its each corneer so from here we have 8* 1/8 = 1 sphere

total sphere = 4

now raius is linked with the unit cell length = r = A/2* 2^1/2 (A=564 pm)

r= 564/2*2^1/2 = 199.4 pm

now volume covered by 4 spheres = 4 * 4/3 * 3.14 *r^3

= 4* 4/3 * 3.14 *199.4^3= 133772474 pm^3

now volume of unit cell = A ^3 =564^3 = 179406144 pm^3

now empty space = unit cell 's volume - total volumes of sphere

= 179406144-133772474= 45633670 pm ^3

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