Calculate the number of unit cells in 0.3 g of a species having density of `8.5 g//cm^3` and unit cell edge length `3.25×10^(-8)` cm.

Answer

To calculate the number of unit cells in 0.3 g of a species with a density of 8.5 g/cm³ and a unit cell edge length of 3.25 × 10^(-8) cm, we can follow these steps:

### Step 1: Calculate the Volume of a Single Unit Cell
The volume \( V \) of a cubic unit cell can be calculated using the formula:
\[ V = a^3 \]
where \( a \) is the edge length of the unit cell.

Given:
\[ a = 3.25 \times 10^{-8} \text{ cm} \]

Calculating the volume:
\[ V = (3.25 \times 10^{-8})^3 = 3.44 \times 10^{-24} \text{ cm}^3 \]

### Step 2: Calculate the Mass of the Substance
We know the mass of the species is given as:
\[ \text{mass} = 0.3 \text{ g} \]

### Step 3: Calculate the Volume of the Substance
Using the density formula:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
we can rearrange this to find the volume:
\[ \text{volume} = \frac{\text{mass}}{\text{density}} \]

Substituting the known values:
\[ \text{volume} = \frac{0.3 \text{ g}}{8.5 \text{ g/cm}^3} = 0.035294 \text{ cm}^3 \]

### Step 4: Calculate the Number of Unit Cells
The number of unit cells \( N \) can be calculated by dividing the total volume of the substance by the volume of a single unit cell:
\[ N = \frac{\text{volume of substance}}{\text{volume of unit cell}} \]

Substituting the values:
\[ N = \frac{0.035294 \text{ cm}^3}{3.44 \times 10^{-24} \text{ cm}^3} \approx 1.03 \times 10^{21} \]

### Final Answer
The number of unit cells in 0.3 g of the species is approximately:
\[ N \approx 1.03 \times 10^{21} \]

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