Explain why there are two elements in the first period of the periodic table (hydrogen and helium) and eight elements in the second period.

The periodic table is organized based on the electron configuration of atoms. The first period of the periodic table contains two elements, hydrogen and helium, because the first electron shell of an atom can hold up to two electrons.

Here are the steps to understand this:

1. The first shell of an atom, also known as the 1s orbital, can hold up to two electrons. Hydrogen has one electron in this shell, and helium has two, filling the shell to its capacity.

2. After the first shell is filled, electrons begin to fill the second shell. The second shell has both an 's' and a 'p' orbital. The 's' orbital can hold 2 electrons and the 'p' orbital can hold 6 electrons.

3. Therefore, the second period of the periodic table contains eight elements. The first two elements, Lithium and Beryllium, have their additional electrons in the 2s orbital. The next six elements, from Boron to Neon, have their additional electrons in the 2p orbital.

4. This pattern continues with the subsequent periods on the periodic table, with each period corresponding to a new electron shell being filled.

So, the number of elements in each period of the periodic table is determined by the number of electrons that can fit in the electron shells.