An element is a substance with a certain specific number of protons at its core, the nucleus. By definition, hydrogen is different than helium because hydrogen always has a single proton in its nucleus, while helium always has two. Silicon has 14, gold has 79, and so on. Elements are placed on the periodic table according to the number of protons they contain per atom. Every time you run into hydrogen, position 1 on the periodic table, it will have a single proton. However, the other parts that make up an atom can vary from one type, or isotope, of an element to another.
Although an element is defined by and gets it name from the number of protons it contains, the number of electrons and neutrons in a given atom of an element can vary. The number of neutrons in the atom determines what isotope of an element you have encountered. Every atom of carbon found in nature will have six protons in its nucleus, but although most of the carbon on Earth will also have six neutrons, a small percent of carbon has seven neutrons instead of six. This is just a natural difference in how the two isotopes are made. In fact, there is an additional naturally occurring carbon isotope on Earth, called carbon-14, which contains yet another neutron, for a total of eight neutrons. This form of carbon is very rare, and because it is slightly radioactive and breaks down over a very well known amount of time, scientists can use the tiny amounts of this element that get trapped in bones and other organic items to date ancient items very accurately. Learn more how radioactive isotopes are used to treat cancer.
Different isotopes of the same element can be either stable, or unstable. An unstable isotope, like carbon-14, has a naturally occurring tendency to break down into another element (in this case, nitrogen-14). To change from one element to another, the number of protons must, of course, change. When six-proton carbon decays to seven-proton nitrogen, it spits out an electron (and another sub-atomic particle called an anti-neutrino). The energy given off by the reaction is known as radioactivity. Unstable isotopes are all, to greater or lesser degrees, radioactive. Some elements have several naturally occurring isotopes: hydrogen has three different isotopes found on Earth, nitrogen only 2. Man made elements, such as Americium, have no naturally occurring isotopes: it only exists on Earth when we create it in a laboratory. The term “isotope” is a way of differentiating between atoms of an element with different numbers of neutrons in the nucleus.