Single crystal silicon consists of three-dimensional arrays of the basic unit cell as shown. (a) How many atoms are in each unit cell? (b) What is the volume of the unit cell in cm3? (c) Show that the atomic density of silicon is 5 × 1022 atoms/cm3. (d) The density of silicon is 2.33g/cm3.What is the mass of one unit cell? (e) Based on your calculations here, what is the mass of a proton? Assume that protons and neutrons have the same mass and that electrons are much much lighter. Is your answer reasonable? Explain.
Single crystal silicon consists of three-dimensional arrays of the basic unit cell as shown. (a) How many atoms are in each unit cell? (b) What is the volume of the unit cell in cm3? (c) Show that the atomic density of silicon is 5 × 1022 atoms/cm3. (d) The density of silicon is 2.33g/cm3.What is the mass of one unit cell? (e) Based on your calculations here, what is the mass of a proton? Assume that protons and neutrons have the same mass and that electrons are much much lighter. Is your answer reasonable? Explain.
- Total number of atoms in unit cell = 8 atoms at corners at 1/8 each cell
+6 atoms in faces at ½ each in cell
+4 atoms within cell.
= (1+3+4)
= 8
So the total number of Si atoms per unit cell is 8.
The dimension of unit cell is (l) = 5.43 Å = 5.43 × 10-8 cm
- The volume of unit cell = l3
= (5.43 × 10-8 cm) 3 cm3
= 16.01 × 10-23 cm3
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