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, d=(M Z/N0 a3) where, Z= number of atoms in unit cell ∴ Z =(d N0 a3/M) =(8.92 × 6.023 × 1023 ×(362 × 10-10)3/63.55) =4.0 Thus, metal has face centred unit cell.

Q. The cubic unit cell of a metal (molar mass $= 63.55 g m o l^{- 1}$ ) 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, $d = \frac{MZ}{N _{0} a ^{3}}$
where, $Z =$ number of atoms in unit cell
$∴ Z = \frac{d N _{0} a ^{3}}{M}$
$= \frac{8.92 \times 6.023 \times 1 0 ^{23} \times ( 362 \times 1 0 ^{- 10} ) ^{3}}{63.55}$
$= 4.0$
Thus, metal has face centred unit cell.

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