InAs is a lll-V semiconductor that has the zinc blende structure with a lattice
ID: 2306596 • Letter: I
Question
InAs is a lll-V semiconductor that has the zinc blende structure with a lattice parameter of 0.606 nm. Given the atomic masses of In (114.82 g mol-1) and As (74.92 g mol-1) find the density. CdO has the NaCI crystal structure with a lattice parameter of 0.4695 nm. Given the atomic masses of Cd (112.41 g mol-1) and O (16.00 g mol-1) find the density. KCI has the same crystal structure as NaCI. The lattice parameter a of KCI is 0.629 nm. The atomic masses of K and Cl are 39.10 g mol-1 and 35.45 g mol-1 respectively. Calculate the density of KCI.Explanation / Answer
(a) atomic mass of In ans As are 114.82g/mol and 74.92 g/mol respectively
114.82/6.02x1023 gram/atom and 74.92/6.02x1023 gram/atom respectively
In As is FCC with four atoms per unit cell
so the mass of In As if the sum of mass of 4 atoms of In and 4 atoms of As
mass of unit cell of InAs= (76.29x10-23 +49.78x10-23 )gram =126.07x10-23 gram
volume of unit cell= cube of lattice parameter=(0.606x10-9 )3 =222.54x10-30 m3
thus density= mass/volume= 0.566x107 gram/m3 = 5.67gram/cm3
(b) CdO is FCC with four atoms per unit cell
atomic masses of Cd and O are=112.41g/mol and 16 g/mol respectively
=112.41/6.02x1023 g/atom and 16/6.02x1023 g/atom
mass of 4 atoms of Cd and 4 atoms of O are= 74.69x10-23 gram and 10.63x10-23 gram respectively
mass of unit cell of CdO= (74.69+10.63)x10-23 =85.32x10-23 gram
volume of unit cell is cube of lattice parameter= (0.4695x10-9 )3 =0.1034x10-27 m3
thus density= mass/volume = 85.32x10-23 gram /0.1034x10-27 =825.14x104 g/m3 =8.25gram/cm3
(c) KCl has FCC structure
it has 4 atoms per unit cell.
lattice parameter for KCl is=0.629 nm
atomic masses of K and Cl are= 39.10g/mo and 35.45g/mol respectively
=39.10/6.02x1023 g/atom and 35.45/6.02x1023 g/atom respectively
so the mass of 4 atoms of K and 4 atoms of cl are=25.98x10-23 gram and 23.55x10-23 gram
thus the mass of unit cell of KCl=(25.98+23.55)x10-23 gram =49.53x10-23 gram
volume of unit cell is cube of lattice parameter= (.629x10-9 )3 =2.48x10-28 m3
thus the density of KCl is =49.53x10-23 /2.48x10-28 = 19.97x105 gram/m3 =1.997gram/cm3