Answer:
Explanation:
When α = β = γ = 90 and a = b = c, we have a cubic lattice, but if we make c larger than a and b ( a= b) we have a tetragonal lattice.
You can see that this lattice is similar to the cubic lattice, the simplest one, which can be simple or primitive cubic or body centered. Similarly the tetragonal lattice can be primitive and body centered lattice.
When they tell us that there are atoms at all the corners and also one at the center of the unit cell we deduce that the unit cell is body centered lattice.
b). For the density calculation, we need to know the mass and the volume of the unit cell.
Number of atoms/ unit cell:
8 atoms x 1/8 = 1
1 center
Therefore we have 2 atoms per unit cell.
The mass is:
= 123 g / mol x 1 mol / 6.022 x 10²³ x 2 atoms/unit cell
= 4.1 g x 10⁻²² g/unit cell
The volume is given by V = a x b x c
Lets convert the dimensions to cm since the density is commonly expressed in g/cm³:
0.298 nm x 1 cm / 10⁷ cm = 2.98 x 10⁻⁸ cm
Then,
V = 2.98 x 10⁻⁸ cm x 2.98 x 10⁻⁸ cm x 4.80 x 10⁻⁸ cm
V = 4.3 x 10⁻²³ cm³
Finally the density is
d = m/V= 4.1 x 10⁻²² g /4.3 x 10⁻²³ cm³ = 9.5 g/cm³
