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JEE Main202310 Apr 2023Evening ShiftChemistrySolid StateActual

The correct relationships between unit cell edge length ‘ a ’ and radius of sphere ‘ r ’ for face-centred and body-centred cubic structures respectively are:

Options

  1. A2 2 r = a and 3 r = 4 a
  2. Br = 2 2 a and 4 r = 3 a
  3. Cr = 2 2 a and 3 r = 4 a
  4. D2 2 r = a and 4 r = 3 a

Correct answer

D. 2 2 r = a and 4 r = 3 a

Step-by-step solution

A face-centered cubic (fcc) unit cell contains a component in the center of each face in addition to those at the corners of the cube. The atoms touch each other along the face diagonal. For   FCC :     a 2 = 4 r a = 2 2 r A body-centered cubic (bcc) unit cell contains a component in the center of the cube in addition to those at the corners of the cube. The atoms touch each other along the body diagonal. For BCC   :   a 3 = 4 r

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