Most elements, except for a few like plutonium which was made artificially, are created in the universe by stars, supernovas and other phenomenon.
Hydrogen, helium and traces of lithium were created a few minutes after the big bang. At that time, it was very hot, so protons, electrons and neutrons (which had newly formed) could fly around freely. Normally, two protons do not bump into each other and stick together because they have the same polarity. They are both positive. But at that time it was so hot that protons could easily bump into each other and stick together.
All the hydrogen we know of was created a few moments after the big bang. But as stars use this most basic element to make more complex ones the universe could run out. Gladly this will not happen because of radioactive decay.
Helium ,the second most abundant element in the universe after hydrogen, was not only created a few minutes after the big bang but also in stars with the proton proton chain (fusion of hydrogen into helium).
Unlike most elements lithium is not created in stars, only in white dwarfs (dead stars), and that is why it is not one of the most abundant elements even though traces of it were created just after the big bang.
All those elements were created by fusion in stars.
More information in the blog entry life of a star.Most elements heavier then iron are created in the (slow neutron capture)s-process when an atom heavier than helium gets bombarded with neutrons. These neutrons are created when carbon13 or neon22 atoms are bombarded with alpha particles (helium cores). These neutrons then transform into protons and make new elements.
In stars this process happens between the hydrogen and helium layer. The process stops at lead.
Elements heavier than lead are created in the (rapid neutron capture)r-process which is the same as the s-process but faster and with more neutrons. This process happens in supernovas.
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