How is it proved that alpha rays are nuclei of Helium atoms?

The identification is made by Rutherford and Royds in 1909. By spectroscopic method, they found traces of Helium in a pure sample of Radon gas, which is an alpha emitter. When an electric discharge was passed through a tube containing pure radon gas, initially only characteristic Radon lines appeared.

After a day, Rutherford found that Radon lines became somewhat weaker and new lines started appearing. These new lines were identified with Helium spectrum. As the days passed, the Radon spectrum began weakening while Helium lines grow brighter.

Thus, for first time, people saw decay of an element (Radon) and birth of a new element, Helium nuclei. Such a transformation in which a parent element gives rise to a new element called daughter product by emitting radioactive rays is called radioactive transformation.