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Prout's hypothesis was an early 19th century attempt to explain the existence of the various chemical elements through a hypothesis regarding the internal structure of the atom. In 1815 and 1816, the English chemist William Prout published two papers in which he observed that the atomic weights that had been measured for the elements known at that time appeared to be integer multiples of the atomic weight of hydrogen. He then hypothesized that the hydrogen atom was the only truly fundamental object, and that the atoms of other elements were actually groupings of various numbers of hydrogen atoms.

Prout's hypothesis remained influential in chemistry throughout the 1820s. However, more careful measurements of the atomic weights, such as those compiled by Jöns Jakob Berzelius in 1828 or Edward Turner in 1832, "disproved" the hypothesis. In particular the atomic weight of chlorine, which is 35.45 times that of hydrogen, could not at the time be explained in terms of Prout's hypothesis.

The discrepancy in the atomic weights was later understood to be the result of multiple isotopes of the same element. Although all elements are the product of nuclear fusion of hydrogen into higher elemets, it is now understood that atoms consist of both protons (hydrogen nuclei) and neutrons. Protons in nuclei decay into neutrons by emition of beta radiation.

The modern version of Prout's rule is that the atomic mass of a nucleus of proton number P and neutron number N is equal to sum of the masses of its constituent protons and neutrons minus its binding energy.

• William Prout (1815). On the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms. Annals of Philosophy, 6: 321–330. Online reprint
• William Prout (1816). Correction of a mistake in the essay on the relation between the specific gravities of bodies in their gaseous state and the weights of their atoms. Annals of Philosophy, 7: 111–13. Online reprint
• The Semiempirical Formula for Atomic Masses

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