The unit cell for tin has tetragonal symmetry, with a and b lattice parameters of 0.583 and 0.318 nm, respectively. If the density, atomic weight, and atomic radius are 7.30 g/cm3, 118.69 g/mol, and 0.151 nm, respectively, compute the atomic packing factor.
Answers & Comments
Answer:
To calculate the atomic packing factor (APF) for a tetragonal unit cell, you can use the formula:
APF = (Number of atoms per unit cell) * (Volume of a single atom) / (Volume of the unit cell)
Here are the given parameters:
- Lattice parameters a = 0.583 nm and b = 0.318 nm
- Atomic radius (r) = 0.151 nm
First, you need to find the volume of the unit cell:
Unit cell volume (V_unit cell) = a * a * b
Now, calculate the volume of a single atom using the atomic radius:
Volume of a single atom (V_atom) = (4/3) * π * r^3
Next, determine the number of atoms in the tetragonal unit cell:
Since the unit cell is tetragonal, there are 8 corner atoms and one atom at the center of the bottom face. So, there are a total of 9 atoms in a tetragonal unit cell.
Now, you can calculate the atomic packing factor (APF):
APF = (Number of atoms per unit cell) * (Volume of a single atom) / (Volume of the unit cell)
APF = (9) * (V_atom) / (V_unit cell)
Substitute the values and calculate the APF. Make sure to convert all lengths to the same units, such as nanometers (nm) for consistency. Once you've computed the APF, you'll have the answer.