Who figured out that different isotopes have different numbers of neutrons?
From Pauling's &quot;General Chemistry&quot; (ref. 1):

In 1921 the American chemist W.D. Harkins described nuclei as being built of protons and neutrons; he used the word &quot;neutron&quot; for a hypothetical particle with mass equal to that of the proton and with no electric charge. Ernest Rutherford made a similar suggestion during the same year. In 1932 the discovery of tne neutron was reported by the English physicist James Chadwick (born 1891).

The original article in which Harkins (ref. 2) reported this hypothesis is linked by the Wikipedia:
References

Linus Pauling, General Chemistry, second edition, 1970, p. 102
Harkins, William (1921). &quot;The constitution and stability of atomic nuclei. (A contribution to the subject of inorganic evolution.)&quot;. Philos. Mag. 42 (249): 305.