A cubic unit cell of a metal with molar mass of $63.55 g m o l^{- 1}$ has an angle length of $362 p m$ . Its density is $8, 92 g c m^{- 3}$ . The type of unit cell is:

primitive

No worries! We‘ve got your back. Try BYJU‘S free classes today!

face centred

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

end centred

No worries! We‘ve got your back. Try BYJU‘S free classes today!

body centred

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B face centred
$D e n s i t y = \frac{Z \times M}{a^{3} \times N_{A}}$
$Z = \frac{d \times N_{A} \times a^{3}}{M}$
$= \frac{8.92 \times 6.023 \times 10^{23} \times (362 \times 10^{- 10})^{3}}{63.55} = 4$
Now, the face-centered cubic ( $f c c$ ) contains 4 atoms per unit cell.
$∴$ The metal crystallises in $f c c$ .

Suggest Corrections

Similar questions

Q. An element with molar mass

27 g m o l^{- 1}

forms a cubic unit cell with edge length

4.05 \times 10^{- 8} c m

. If its density is

2.7 g c m^{- 3}

, what is the nature of the cubic unit cell?

Q. Lithium metal has a body centred cubic structure. Its density is

0.53 g c m^{- 3}

and its molar mass is

6.94 g m o l^{- 1}

. Calculate the edge of a unit cell of Lithium metal.

Q. Lithium metal has a body centred cubic structure. Its density is

0.53 g c m^{- 3}

and its molar mass is

6.94 g m o l^{- 1}

. Calculate the volume of a unit cell of lithium metal.

An element with molar mass 2.7 × 10^-2 kg mol^-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 103 kg m⁻³, what is the nature of the cubic unit cell?

Q. The density of chromium metal is

7.2 {g cm}^{- 3}

. If the unit cell is cubic with an edge length of 289 pm, determine the type of unit cell (simple, body centred or face centred). [Atomic mass of

C r = 52 amu, N_{A} = 6.02 \times 10^{23} {mol}^{- 1}]

Join BYJU'S Learning Program

A cubic unit cell of a metal with molar mass of 63.55 g mol−1 has an angle length of 362 pm. Its density is 8,92 g cm−3. The type of unit cell is:

The correct option is B face centredDensity=Z×Ma3×NAZ=d×NA×a3M=8.92×6.023×1023×(362×10−10)363.55=4Now, the face-centered cubic (fcc) contains 4 atoms per unit cell.∴The metal crystallises in fcc.

A cubic unit cell of a metal with molar mass of $63.55 g m o l^{- 1}$ has an angle length of $362 p m$ . Its density is $8, 92 g c m^{- 3}$ . The type of unit cell is: