Which of the following expressions is correct | vedclass

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(C) In a $CsCl$ crystal structure,$Cl^{-}$ ions are located at the corners of a simple cubic unit cell,and the $Cs^{+}$ ion is located at the body cen

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$r_c + r_a = \frac{\sqrt{3} a}{2}$

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(C) In a $CsCl$ crystal structure,$Cl^{-}$ ions are located at the corners of a simple cubic unit cell,and the $Cs^{+}$ ion is located at the body center.Along the body diagonal of the cube,the $Cs^{+}$ ion and the $Cl^{-}$ ions at the corners touch each other.The length of the body diagonal of a cube with edge length $a$ is given by $\sqrt{3} a$.Since the body diagonal passes through two $Cl^{-}$ ions (at corners) and one $Cs^{+}$ ion (at the center),the length of the body diagonal is equal to $2r_a + 2r_c = 2(r_c + r_a)$.Equating the two expressions: $2(r_c + r_a) = \sqrt{3} a$.Therefore,$r_c + r_a = \frac{\sqrt{3} a}{2}$.

Which of the following expressions is correct in case of a $CsCl$ unit cell (edge length,$a$)?

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