The cubic unit cell of a metal (molar mass =63 ⋅ 55 g mol -1 ) has an edge length of 362 pm. Its density is 8.92 g cm -3 the type of unit cell is

Question

The cubic unit cell of a metal (molar mass =63 ⋅ 55 g mol -1 ) has an edge length of 362 pm. Its density is 8.92 g cm -3 the type of unit cell is (A) Primitive (B) Face centred (C) Body centred (D) End centred

Tardigrade Admin · Accepted Answer

Density =(Z × M/a3 × NA) Z=(d × NA × a3/M) =(8.92 × 6.023 × 1023 ×(362 × 10-10)3/63.55)=4 Now, the face-centered cubic (fcc) contains 4 atoms per unit cell. ∴ The metal crystallises in fcc.

Q. The cubic unit cell of a metal (molar mass $= 63 \cdot 55 g m o l^{- 1}$ ) has an edge length of $362 p m$ . Its density is $8.92 g c m^{- 3}$ the type of unit cell is

Primitive

Face centred

Body centred

End centred

Density $= \frac{Z \times M}{a ^{3} \times N _{A}}$
$Z = \frac{d \times N _{A} \times a ^{3}}{M}$
$= \frac{8.92 \times 6.023 \times 1 0 ^{23} \times ( 362 \times 1 0 ^{- 10} ) ^{3}}{63.55} = 4$
Now, the face-centered cubic (fcc) contains $4$ atoms per unit cell.
$∴$ The metal crystallises in fcc.

Q. The cubic unit cell of a metal (molar mass =63⋅55gmol−1 ) has an edge length of 362pm. Its density is 8.92gcm−3 the type of unit cell is