The density of sodium chloride at `25^(@)C "is" 2.163 xx 10 ^(3) " kg m" ^(-3)` When X -rays rom a palladium target having waveleth of 58.1 pm are used, the (200) reflection of sodium chloride occurs at an angle of ` 5.90^(@)` . How many `Na^(+) and Cl^(-)` ions are present in the unit cell ? ( Molar mass of NaCl = 58.5 `" mol" ^(-1) sin 5.9 ^(@) = 0.1028)`

Explanation

` 2 d sin theta = n lambda`
for n =1 , ` d_(200) = lambda/(2 sin theta) = ( 58.1"pm")/ (2sin 5.9^(@)) = 58.1/(2xx 0.1028) ` = 282 pm
` d_(200) = a/(sqrt(h^(2) + k^(2) +l^(2)))`
` 282 "pm" = a /( sqrt(2^(2) + 0^(2)+0^(2))) = a/2 or a = 564 ` pm
` p = ( Z xx M)/( a^(3) xx N_(0))`
` Z = ( pxx a^(3) xx N_(0)) / M = ((2.163 xx 10^(3) " kg m"^(-3)) ( 564 xx 10^(-12) m)^(3) ( 6.023 xx 10^(23) "mol"^(-1)))/ ( 58.5 xx 10^(-3) " kg mol" ^(-1)) `
3.999 = 4
Thus , a unit cell contains 4 NaCl unit s or 4 ` Na ^(+)` ions and ` 4 Cl^(-)` ions .