Calcium crystallizes in a face centred cubic unit cell with a text= text0 text.560 textnm text. The density of the metal if it contains 0.1% schottky defects would be:

Question

Calcium crystallizes in a face centred cubic unit cell with a text= text0 text.560 textnm text. The density of the metal if it contains 0.1% schottky defects would be: (A)  text1 text.51 gcm text-3 (B)  text2 text.51 gcm text-3 (C)  text15 text.1 gcm text-3 (D)  text0 text.151 gcm text-3

Tardigrade Admin · Accepted Answer

A face centred cubic unit cell contains four atoms. Schottky defect is basically a vacancy defect in ionic solids. Due to Schottky defects, the vacant spaces will increase, resulting in decrease in number of atoms per unit cell.
Thus, number of atoms will reduce to:

Z = (4 - \frac{4 \times 0.1}{100}) = 3.996

The density of the metal can be calculated by:

ρ = \frac{Z \times M}{N _{0} \times a ^{3}}

Where,

M

is the molecular mass of calcium

= 40 g m o l^{- 1}

N_{0}

is the Avogadro number

= 6.022 \times 1 0^{23} m o l^{- 1}

a

is the edge length

= 0.560 nm = 0.56 \times 1 0^{- 7} c m

Putting the values in the formula above:

= \frac{3.996 \times ( 40 g m o l ^{- 1} )}{( 0.560 \times 1 0 ^{- 7} c m ) ^{3} \times ( 6.022 \times 1 0 ^{23} m o l ^{- 1} )}

= 1.51 g c m^{- 3}

Q. Calcium crystallizes in a face centred cubic unit cell with a $= 0 .560 nm .$ The density of the metal if it contains 0.1% schottky defects would be:

$1 .51 gcm^{-3}$

$2 .51 gcm^{-3}$

$15 .1 gcm^{-3}$

$0 .151 gcm^{-3}$

Q. Calcium crystallizes in a face centred cubic unit cell with a =0.560nm. The density of the metal if it contains 0.1% schottky defects would be:

1.51 gcm-3

2.51gcm-3

15.1 gcm-3

0.151 gcm-3

Q. Calcium crystallizes in a face centred cubic unit cell with a $= 0 .560 nm .$ The density of the metal if it contains 0.1% schottky defects would be:

$1 .51 gcm^{-3}$

$2 .51 gcm^{-3}$

$15 .1 gcm^{-3}$

$0 .151 gcm^{-3}$