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Potassium fluoride has structure. Its ...

Potassium fluoride has structure. Its density `2.48 gm^(-3)`is and its molar mass is 58 `"gmol"^(-1)` Compute the distance in picometer between `K^(+)` and `F^(-)` ions in (Given that `(155.318)^(1//3)` =5.375), Atomic mass K = 39, F = 19

A

134.35pm

B

268.7 pm

C

403.05 pm

D

201.52 pm

Text Solution

Verified by Experts

The correct Answer is:
B
Since NaCl has f.c.c. structure, KF has also fcc structure and Z=4.
Further in a face centred cubic lattice the distance between the cation and anion is equal to the sum of their radii which is equal to half of the edge length of the unit cell i.e.,`r^(+)+r^(-)`=a//2.
Now edge length `a^(3)=(ZtimesM)/(rhotimesN_(A))`
`=(4times58)/(2.48times6.023times10^(23))=155.318times10^(-24)cm^(3)`
`thereforea=5.375times10^(-8)cm=5.375times10^(-10)m`
`=537.5times10^(-12)=537.5 "pm"`
`"Now" r^(+)+r^(-)=a//2=(537.5)/2=268.7"pm"`
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