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JEE Main 202310 AprilEvening Shift

Exam: JEE Main
Year: 2023
Date: 10 April
Shift: Evening Shift
Subject: Chemistry
Chapter: Solid State

JEE Main 2023 · 10 April · Evening Shift · Chemistry · Solid State

The correct relationships between unit cell edge length ‘ a...

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

A $2\sqrt{2}r = a$ and $\sqrt{3}r = 4a$
B $r = 2\sqrt{2}a$ and $4r = \sqrt{3}a$
C $r = 2\sqrt{2}a$ and $\sqrt{3}r = 4a$
D $2\sqrt{2}r = a$ and $4r = \sqrt{3}a$

Correct answer

D. $2\sqrt{2}r = a$ and $4r = \sqrt{3}a$

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 $FCC: a\sqrt{2} = 4r$
$a = 2\sqrt{2}r$
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 $BCC: a\sqrt{3} = 4r$

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