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Magnesium oxide (mgo) has the rock salt crystal structure and a density of 3.58 g/cm3. the atomic weights of magnesium and oxygen are 24.31 g/mol and 16.00 g/mol, respectively. (a) determine the unit cell edge length.

Sagot :

Answer:

(a)  The unit cell edge length 0.421 nm

Explanation:

Lets calculate -:

Given -

density = [tex]3.58g/cm^3[/tex]

Molecular weight of MgO = 24.31 +16

                                           [tex]40.13 g/mole[/tex]

Avagadro number = [tex]6.022\times10^2^3[/tex]

In rock salt structure , there are four anions and four cations , hence Z=4 (Number of formula per unit cell)

Now, using the formula -

                     [tex]d=\frac{ZM}{N_Aa^3}[/tex]

               [tex]a=[\frac{ZM}{N_Ad}]]^\frac{1}{3}[/tex]

Now, putting the given values

   [tex]a=\frac{4\times40.13g/mole}{6.022\times10^2^3\times(3.58g/cm^3)}[/tex]

  [tex]4.21\times10^-^8 cm[/tex]

  = 0.421 nm

Hence , the unit cell edge length = 0.421 nm

Lanuelidn

The unit cell edge length of magnesium oxide (MgO) is equal to 0.421 nanometer.

Given the following data:

  • Density = 3.58 [tex]g/cm^3[/tex]
  • Atomic weight of magnesium = 24.31 g/mol.
  • Atomic weight of oxygen = 16.00 g/mol.

Scientific data:

  • Avogadro's number = [tex]6.02 \times 10^{23}[/tex]
  • Z for FCC = 4
  • Molar mass of magnesium oxide (MgO) = [tex]24.31 + 16 = 40.31 \;g/mol.[/tex]

To determine the unit cell edge length:

Mathematically, the unit cell edge length for a face-centered cubic (FCC) structure is given by the formula:

[tex]a=\sqrt[3]{\frac{ZM}{\rho N_A} }[/tex]

Where:

  • Z is the number of atoms per unit cell.
  • [tex]\rho[/tex] is the density.
  • M is the molar mass.
  • [tex]N_A[/tex] is the Avogadro constant.

Substituting the given parameters into the formula, we have;

[tex]a=\sqrt[3]{\frac{4 \; \times \;40.31}{3.58\; \times \;6.02 \times 10^{23}} }\\\\a=\sqrt[3]{\frac{161.24}{2.16 \times 10^{24}}}\\\\a=\sqrt[3]{7.47 \times 10^{-23}} \\\\a=4.21 \times 10^{-8}\;meter[/tex]

Note: [tex]1 \;nanometer = 1 \times 10^{-9} \;meter[/tex]

a = 0.421 nanometer.

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