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JEE Advanced levelSingle correct optionDifficulty 3 of 3ss086

In a rock-salt type crystal $MX$ of edge length $540 pm$ the anions are in contact along the face diagonal. Taking $2 = 1.414$ , the radius of the cation in pm is

A191
B135
C79
D175

Answer: C

Anion contact:

2 a = 4 r_{-}

, so

r_{-} = 540/2.828 = 190.9 pm

. Along the edge

a = 2 r_{-} + 2 r_{+}

, so

r_{+} = 270 - 190.9 = 79.1 \approx 79 pm

.

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