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Question: Crystalline CsCshas density \(3.988gcm^{- 3}.\) The volume occupied by single CsCl ion pair in the c...

Crystalline CsCshas density 3.988gcm−3.3.988gcm^{- 3}. The volume occupied by single CsCl ion pair in the crystal will be

A

7.014×10−3cm37.014 \times 10^{- 3}cm^{3}

B

7.014×10−23cm37.014 \times 10^{- 23}cm^{3}

C

1.014×10−3cm31.014 \times 10^{- 3}cm^{3}

D

1.542×10−5cm31.542 \times 10^{- 5}cm^{3}

Answer

7.014×10−23cm37.014 \times 10^{- 23}cm^{3}

Explanation

Solution

For scc, Z = 1

Vol. of unit cell = Vol. of single CsCl ion pair

d=Z×MNA×a3d = \frac{Z \times M}{N_{A} \times a^{3}}

a3=Z×Md×NA=1×168.43.988×6.023×1023=7.014×10−23cm3a^{3} = \frac{Z \times M}{d \times N_{A}} = \frac{1 \times 168.4}{3.988 \times 6.023 \times 10^{23}} = 7.014 \times 10^{- 23}cm^{3}