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Question: The distance between \(Na^{+}\)and \(Cl^{-}\)ions in NaCl with a density \(2.165gcm^{- 3}is\)...

The distance between Na+Na^{+}and ClCl^{-}ions in NaCl with a density 2.165gcm3is2.165gcm^{- 3}is

A

564 pm

B

282 pm

C

234 pm

D

538 pm

Answer

282 pm

Explanation

Solution

d=Z×Ma3×NAd = \frac{Z \times M}{a^{3} \times N_{A}}

a3=Z×Md×NA=4×58.82.165×6.023×1023a^{3} = \frac{Z \times M}{d \times N_{A}} = \frac{4 \times 58.8}{2.165 \times 6.023 \times 10^{23}}

a3=179.5×1024cm3a^{3} = 179.5 \times 10^{- 24}cm^{3}

a=5.64×108a = 5.64 \times 10^{- 8}cm or 564 pm

Distance between Na+Na^{+}and ClCl^{-}

=a2=5642=282pm= \frac{a}{2} = \frac{564}{2} = 282pm