Paragraph: In a cubic unit cell, atoms (A) are present at all...

Paragraph: In a cubic unit cell, atoms (A) are present at all corners, (B) are present at alternate face centre and all edge centres. Atoms (C) are present at face centres left from (B) and one at each body diagonal at distance of

1 / 4^{\text{th }}

of body diagonal from corner.Question: Formula of given solid is

Options

A $\mathrm{A}_3 \mathrm{~B}_8 \mathrm{C}_7$
B $\mathrm{AB}_4 \mathrm{C}_6$
C $\mathrm{A}_6 \mathrm{~B}_4 \mathrm{C}_8$
D $\mathrm{A}_2 \mathrm{~B}_9 \mathrm{C}_{11}$

Correct answer

B. $\mathrm{AB}_4 \mathrm{C}_6$

Step-by-step solution

Atoms

\mathrm{A}(

at corner

)=8 \times \frac{1}{8}=1

Atoms

B=2

(alternate face centre)

\times \frac{1}{2}+12(\text { edge centre }) \times \frac{1}{4}=4

Atoms

C=4

(face centre left from B)

\times \frac{1}{2}+1 \times 4(\text { body diagonal })=6\therefore

Formula

\mathrm{AB}_4 \mathrm{C}_6

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