The ideal crystal structure of a hexagonal close-packed (HCP) crystal consists of layers of atoms arranged in a hexagonal pattern. This crystal structure can be visualized as a stack of close-packed hexagonal layers, with each layer offset from the previous one by half of the interlayer spacing. In an HCP crystal, there are two types of lattice parameters: the long unit cell dimension, denoted as "c", and the short unit cell dimensions, denoted as "a".

Explanation:

1. HCP Crystal Structure:
- The HCP crystal structure is one of the most common crystal structures in nature and is found in many metals and alloys, such as titanium and magnesium.
- In an HCP crystal, the atoms are arranged in a close-packed hexagonal lattice, with each atom surrounded by six nearest neighbors forming an equilateral triangle.
- The layers of atoms in an HCP crystal are stacked in an ABAB... pattern, where each A layer is directly above a B layer. This stacking sequence results in a hexagonal unit cell.

2. Lattice Parameters:
- In an HCP crystal, the long unit cell dimension "c" is the distance between two adjacent layers along the vertical direction. It is also equal to the height of the unit cell.
- The short unit cell dimensions "a" are the distances between neighboring atoms within a layer. These dimensions are equal to the side lengths of the hexagonal unit cell.

3. Relationship between c and a:
- The ratio between the long and short unit cell dimensions of an ideal HCP crystal can be determined using trigonometry.
- In an HCP crystal, the hexagonal unit cell can be visualized as two interpenetrating triangular lattices. The distance between adjacent atoms within a layer (a) can be related to the height of the unit cell (c) using the trigonometric relationship: c = 2 * a * sqrt(6) / 3.
- Solving this equation for the ratio c/a gives: c/a = sqrt(8/3) ≈ 1.633.

4. Determining the Correct Answer:
- Comparing the given options, we can see that the correct answer is option 'C', which is approximately equal to 1.633.
- This ratio represents the ideal relationship between the long and short unit cell dimensions in an HCP crystal structure.

In summary, the ratio of long and short unit cell dimensions in an ideal HCP crystal structure is approximately 1.633. This ratio is derived from the trigonometric relationship between the height of the unit cell and the distance between neighboring atoms within a layer.