Element well in periodic table

The periodic table is arranged in vertical columns called groups and horizontal rows called periods. As you have noticed, different rows contain different numbers of elements, and the the columns are arranged so that there are gaps in the middle of the rows. Why is this ?

The electrons that surround the atoms of each element are arranged into layers called shells. There is a fixed maximum number of electrons in each shell. The innermost shell can contain at most two electrons, which is why the first row only contains two elements, hydrogen (atomic number $1$) and helium (atomic number $2$). The maximum number of electrons in each shell increases as you go outwards from the nucleus, which is why the rows become longer as you move down the table - rows $2$ and $3$ contain $8$ elements each, and rows $4$ and $5$ contain $18$ elements each.

So why are there gaps in the rows ? Why not shuffle all the cells in each row to the left hand side, so that for example helium is above beryllium. After all, both of these elements contain two electrons in their outermost shell.

The columns are arranged so that elements with similar chemical behaviours line up in the same column. And it turns out that the most important single factor that determines the chemical behaviour of an element is not how many electrons are in the outermost shell, but how close the outermost shell of electrons is to being a complete shell.

Hydrogen has similar chemical behaviour to lithium and sodium because all of these elements have just one electron in their outermost shell. So we put hydrogen, lithium and sodium in the same group, which is the left hand column. But helium, with two electrons in its outermost shell, has similar chemical behaviour to neon and argon, with eight electrons in their outermost shells, because all of these elements have a full outermost shell. So we put helium, lithium and argon in the same group, which is the right hand column.

We are used to this "traditional" design for the periodic table, but it is not the only possible design. Various alternative designs have been proposed - see this Wikipedia article for a summary. In particular, French engineer Charles Janet proposed a "left-step" arrangement which avoids the gaps in the rows. In Janet's left-step arrangement, helium does sit immediately above beryllium.