WBJEE · Chemistry · Solid State

Suppose the mass of a single Ag-atom is \(m\). Ag metal crystallises in fcc lattice with unit cell of length \(a\). The density of Ag metal in terms of \(a\) and \(m\) is

A \(\frac{4 m}{a^{3}}\)
B \(\frac{2 m}{a^{3}}\)
C \(\frac{m}{a^{3}}\)
D \(\frac{m}{4 a^{3}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{4 m}{a^{3}}\)

Step-by-step Solution

Detailed explanation

Given that, Mass of single Ag-atom \(=m\) Unit cell length \(=a\) Total atoms present per unit cell of fcc lattice \(=4\) Therefore, mass of unit cell becomes \(4 \mathrm{m}\). Volume of unit cell \(=a^{3}\) Density…

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.

Same subject

Explore more questions on app

From WBJEE

Explore more questions on app