Solid State - Result Question 28

28. Which of the following statement(s) is/are correct?

(1998, 2M)

(a) The coordination number of each type of ion in $CsCl$ crystal is $8$

(b) A metal that crystallises in bcc structure has a coordination number of $12$

(c) A unit cell of an ionic crystal shares some of its ions with other unit cells

(d) The length of the unit cell in $NaCl$ is $552 \hspace{2mm} pm$.

$\left(r _{Na^{+}}=95 \hspace{2mm} pm ; r _{Cl^{-}}=181 \hspace{2mm} pm\right)$

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Answer:

Correct Answer: 28. (a, c, d)

Solution:

  1. (a) The unit cell of $CsCl$ has bcc arrangement of ions in which each ion has eight oppositely charged ions around it in the nearest neighbours as shown below :

<img src=“https://temp-public-img-folder.s3.amazonaws.com/sathee.prutor.images/sathee_image/cropped_2024_01_16_b4fdca9f34924034e8d8g-140_jpg_height_247_width_341_top_left_y_1561_top_left_x_1425.jpg"width="200">

(b) In bcc, coordination number of atom is $8$ .

(c) In an unit cell, a corner is shared in eight unit cells and a face centre is shared between two adjacent unit cells.

(d) In $NaCl$ unit cell; $2\left(r _{Na^{+}}+r _{Cl^{-}}\right)=a$

$ \Rightarrow \quad a=2(95+181)=552 \hspace{2mm} pm $

Hence, $a, c, d$ are correct.