# Sorry, I have one other question. How would I go about solving this problem?

**What fraction of the total volume of a closet packed structure is occupied by atoms? What fraction of the total volume of a simple cubic structure is occupied by atoms?**

Do i need to just plug in examples? I'm not positive on how to go about solving this

## sorry, forgot to mention that its *cubic closest*

## By the way, I made an error in the problem below. There are TWO atoms per unit cell for the body centered cubic structure; therefore, the mass of a single atom is TWICE 47.88*(1/6.022 x 10^23) etc. In cubic closest packing the volume occupied is about 74%.

## I should have said the mass of the UNIT CELL is twice. Of course, the mass of a single atom is what was calculated previously. But you want the mass of a unit cell, not the mass of a single atom of Ti.

## To solve this problem, we need to understand the concept of packing structures and the fraction of volume occupied by atoms.

In a packing structure, atoms are arranged in a regular pattern to form a solid. There are different types of packing structures, such as cubic structures, which include simple cubic, body-centered cubic, and face-centered cubic.

To determine the fraction of the total volume occupied by atoms, we need to consider the number of atoms and the total volume of the structure.

Let's start with the concept of a closet packed structure. In a closet packed structure, the atoms are arranged in a way that maximizes the packing efficiency. These structures are often found in materials like metals. The fraction of the total volume occupied by atoms in a closet packed structure is typically high. In fact, it can be very close to 1, meaning almost all of the volume is occupied by atoms.

Next, let's consider a simple cubic structure. In a simple cubic structure, the atoms are arranged in a cube, with one atom at each corner. To determine the fraction of the volume occupied by atoms, we can calculate the ratio of the volume occupied by atoms to the total volume of the structure.

In a simple cubic structure, each atom only occupies a small portion of the total volume. To calculate the fraction, we need to consider the number of atoms and the size of the unit cell.

For a simple cubic structure, there is only one atom per unit cell, located at each corner. The volume occupied by each atom is equal to the volume of the unit cell. Since the atom is located at the corner, it only occupies one-eighth of the volume of the unit cell. Therefore, the fraction of the total volume occupied by atoms in a simple cubic structure is 1/8.

To summarize:

- In a closet packed structure, the fraction of the total volume occupied by atoms can be almost 1.

- In a simple cubic structure, the fraction of the total volume occupied by atoms is 1/8.

So, to solve the problem, you don't need to plug in specific examples. Instead, you can use the principles and concepts described above to calculate the fractions for each type of structure.