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

`2d sin theta=n lambda`
For n=1, `d_200=lambda/(2 sin theta)="58.1 pm"/(2 sin 5.9^@) =58.1 /(2xx0.1028)`=282 pm
`d_200=a/(sqrt(h^2+k^2+l^2))`
`therefore "282 pm"=a/(sqrt(2^2+0^2+0^2))=a/2` or a=564 pm
`rho=(ZxxM)/(a^3xxN_0)`
or `Z=(rhoxxa^3xxN_0)/M=((2.163xx10^3 "kg m"^(3))(564xx10^(-12)m)^3 (6.023xx10^23 "mol"^(-1)))/(58.5xx10^(-3) "kg mol"^(-1))`
=3.999 `approx` 4
Thus, a unit cell contain 4 NaCl units or 4 `Na^+` ions and 4 `Cl^-` ions.