AP EAMCET · Chemistry · Solid State

If each edge of a cubic unit cell of an element having atomic mass 120 and density \(6.25 \mathrm{~g} \mathrm{cc}^{-1}\) measures \(400 \mathrm{pm}\), then the crystal lattice is

A primitive
B body centered
C face centered
D end centered

Verified Solution

Answer & Solution

Correct Answer

(B) body centered

Step-by-step Solution

Detailed explanation

Atomic weight \((m)=120\) \(N_A=6.022 \times 10^{23}\) Unit cell \((a)=400 \mathrm{pm}\) \(=400 \times 10^{-10} \mathrm{~m}\) As we know \(d=\frac{Z M}{N_A \times a^3}\) \(6.25=\frac{Z \times 120}{6.022 \times 10^{23} \times\left(400 \times 10^{-10}\right)^3}\) \(Z=2\) 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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