Iron crystallizes in several forms. At 1185 K , the body centred cubic `alpha`- form of iron changes to the face centred cubic `gamma`- form of iron. Assuming that the distance betweem the nearest neighbours is the same in two forms at the transition temperature, calcuate the ratio of the density of `alpha`- form to that of `gamma`- form at the transition temperature.

Explanation

To calculate the ratio of the density of the alpha form (body-centered cubic, BCC) to the gamma form (face-centered cubic, FCC) of iron at the transition temperature of 1185 K, we can follow these steps:

### Step 1: Determine the effective number of atoms per unit cell (Z) for both forms.

- **For the alpha form (BCC)**:
- BCC has 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom, and 1 atom at the center.
- Therefore, the total number of atoms \( Z \) in BCC is:
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