The ratio of the volume of a tetragonal lattice unit cell to that of a hexagonal lattice unit cell is (both having same respective lengths)

Options

A. `(sqrt(3))/(2) `abc
B. `(2)/(2sqrt(3))`
C. `(2)/(sqrt(3)) (a^(2))/(b)` c
D. 1

Explanation

To find the ratio of the volume of a tetragonal lattice unit cell to that of a hexagonal lattice unit cell, we can follow these steps:

### Step 1: Understand the Unit Cell Dimensions
In a tetragonal unit cell, the lengths of the edges are given as:
- \( a \) (length of the base edges, where \( a = b \))
- \( c \) (height of the cell)

In a hexagonal unit cell, the dimensions are:
...