AP EAMCET · Chemistry · Solid State

A metal crystallizes with a $FCC$ -lattice, the edge of whose unit cell is $xpm$ . The diameter of this metal atom would be $p m .$

A $2 x$
B $\frac{x}{\sqrt{2}}$
C $x \sqrt{2}$
D $\frac{\sqrt{2}}{x}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{x}{\sqrt{2}}$

Step-by-step Solution

Detailed explanation

In the face-centred unit cell, atoms are arranged at the corners and at centered of the face diagonal. Let radius of metal atom = r So, the distance AC= r+2r+r=4r The distance AD and CD = x Using the Pythagoras theorem, AC2=AD2+CD2AC2=x2+x2=2x24r2=2x22x=4rr=2x4=x22 So, the…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A metal crystallizes with a FCC-lattice, the edge of whose unit cell is xpm. The diameter of this metal atom would be p m .

Step-by-step Solution

A metal crystallizes with a $FCC$ -lattice, the edge of whose unit cell is $xpm$ . The diameter of this metal atom would be $p m .$