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Well, Harry Potter sings it to you.
An element is a substance that is made entirely from one type of atom. For example, the element hydrogen is made from atoms containing a single proton and a single electron. If you change the number of protons an atom has, you change the type of element it is.
In 1869, Dmitri Mendeleev, a Russian scientist at the time, created the very first periodic table. Around this time, there only about 60 elements discovered. Using flash cards with all of the elements' information on it, they played "chemical solitaire" with them, trying to find the best way to organize them. Dmitri tried to organize them by density, appearence, melting point, and others, but he finally settled with atomic mass. Today, the elements are rearranged by the atomic number, which is also the number of protons in the elements' nucleas.
If you had very, very good eyes and could look at the atoms in a sample of hydrogen, you would notice that most of the hydrogen atoms would have no neutrons, some of them would have one neutron and a few of them would have two neutrons. These different versions of hydrogen are called isotopes. All isotopes of a particular element have the same number of protons, but have a different number of neutrons. If you change the number of neutrons an atom has, you make an isotope of that element.
Currently, scientists know of 118 different elements. Some, like gold, silver, copper and carbon, have been known for thousands of years. Others, such as meitnerium, darmstadtium and ununquadium, have only recently been created by scientists.
The periodic table is a table of the chemical elements in which the elements are arranged by order of atomic number in such a way that the periodic properties of the elements are made clear. The standard form of the table includes periods (usually horizontal in the periodic table) and groups (usually vertical). Elements in groups have some similar properties to each other.