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Nuclear fusion is the process of making a single heavy nucleus (part of an atom) from two lighter nuclei. This process is called a nuclear reaction. It releases a large amount of energy. The nucleus made by fusion is heavier than either of the starting nuclei. However, it is not as heavy as the combination of the original mass of the starting nuclei (atoms). This lost mass is changed into lots of energy. This is shown in Einstein's famous E=mc2 equation.
Fusion happens in the middle of stars like the Sun. Hydrogen atoms are fused together to make helium. This releases lots of energy. This energy powers the heat and light of the star. Not all elements can be joined. Heavier elements are less easily joined than lighter ones. Iron (a metal) cannot fuse with other atoms. This is what causes stars to die. Stars join all of their atoms together to make heavier atoms of different types, until they start to make iron. The iron nucleus cannot fuse with other nuclei. The reactions stop. The star eventually will cool down and die.
On Earth it is very difficult to start nuclear fusion reactions that release more energy than is needed to start the reaction. The only successful approach so far has been in nuclear weapons. The hydrogen bomb uses an atomic (fission) bomb in order to start fusion reactions. For over 50 years scientists and engineers have been trying to find a safe and working way of controlling and containing fusion reactions that can generate electricity. They still have many challenges to overcome before it can be used as a clean source of energy.