Question

question 32 of 34
consider a hexagonal close - packed unit cell, as shown in
the image.
how many corner atoms are shown in the image?
number of corner atoms: 12
what fraction of each corner atom is inside the boundaries of
the cell?
fraction inside the cell: $\frac{1}{6}$
how many face atoms are shown in the image?
number of face atoms: 6
what fraction of each face atom is inside the boundaries of
the cell?
fraction inside the cell:
additionally, there are three atoms that are 100% inside the
boundaries of the unit cell.
if you sum all the whole and fractions of atoms, how many
atoms are actually inside a hexagonal close - packed unit cell?
number of atoms inside the cell:

Explanation:

Step1: Face atom fraction definition

Face atoms are shared equally between 2 adjacent unit cells, so the fraction inside one cell is $\frac{1}{2}$.

Step2: Calculate corner atom contribution

Multiply corner count by their fraction:
$12 \times \frac{1}{6} = 2$

Step3: Calculate face atom contribution

Multiply face count by their fraction:
$6 \times \frac{1}{2} = 3$

Step4: Add internal atoms

Add the 3 fully internal atoms to the contributions:
$2 + 3 + 3 = 6$

Answer:

fraction inside the cell: $\frac{1}{2}$
number of atoms inside the cell: 6