Respuesta :
Explanation:
The given data is as follows.
   Mass = 27.9 g/mol
As we know that according to Avogadro's number there are [tex]6.023 \times 10^{26}[/tex] atom present in 1 mole. Therefore, weight of 1 atom will be as follows.
      1 atoms weight = [tex]\frac{38}{6.023 \times 10^{26}}[/tex]  Â
In a diamond cubic cell, the number of atoms are 8. So, n = 8 for diamond cubic cell.
Therefore, total weight of atoms in a unit cell will be as follows.
      = [tex]\frac{8 \times 27.9 g/mol}{6.023 \times 10^{26}}[/tex]
      = [tex]37.06 \times 10^{-26}[/tex]
Now, we will calculate the volume of a lattice with lattice constant 'a' (cubic diamond) as follows.
          = [tex]a^{3}[/tex]
          = [tex](0.503 \times 10^{-9})^{3}[/tex]
          = [tex]0.127 \times 10^{-27} m^{3}[/tex]
Formula to calculate density of diamond cell is as follows.
        Density = [tex]\frac{mass}{volume}[/tex]
               = [tex]\frac{37.06 \times 10^{-26}}{0.127 \times 10^{-27} m^{3}}[/tex]
              = 2918.1 [tex]g/m^{3}[/tex]
or,             = 0.0029 g/cc    (as 1 [tex]m^{3} = 10^{6} cm^{3}[/tex])
Thus, we can conclude that density of given semiconductor in grams/cc is 0.0029 g/cc.
