**Explanation:**

The modern periodic table is organized based on the increasing atomic number of elements. It is divided into rows called periods and columns called groups. Each period represents the energy level or shell in which the electrons of the elements are arranged.

Among the four options provided, the correct answer is option 'A' - Sixth. The sixth period of the periodic table contains 32 elements.

**Understanding Periods:**

1. **What is a period?**
- A period is a horizontal row in the periodic table.
- There are a total of 7 periods in the modern periodic table.
- Each period represents the principal energy level or shell of the elements in that row.

2. **Number of Elements in Each Period:**
- The number of elements in each period varies.
- The first period contains only 2 elements (hydrogen and helium).
- The second period contains 8 elements.
- The third period contains 8 elements.
- The fourth period contains 18 elements.
- The fifth period contains 18 elements.
- The sixth period contains 32 elements.
- The seventh period contains 32 elements.

3. **Why does the Sixth Period have 32 Elements?**
- The sixth period starts with the element cesium (Cs) with atomic number 55 and ends with radon (Rn) with atomic number 86.
- The sixth period includes the filling of the 6s, 4f, 5d, and 6p orbitals.
- The 6s orbital can hold a maximum of 2 electrons, the 4f orbital can hold a maximum of 14 electrons, the 5d orbital can hold a maximum of 10 electrons, and the 6p orbital can hold a maximum of 6 electrons.
- Adding up these electron capacities (2 + 14 + 10 + 6) gives a total of 32 elements in the sixth period.

Therefore, the correct answer is option 'A' - Sixth period, which contains 32 elements.

Sixth period has 32 elements and seventh period is incomplete and has only 29 elements. So answer is a)sixth