The answer came from Einstein in 1906: E = mc2.
By the 1930's the concept of nuclear reactions became accepted.
Compare the mass difference between 4 hydrogen atoms and one helium atom:
6.6466 x 10-27 kg for 1 helium atom
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0.048 x 10-27 kg
This is only 0.7% of the mass, but if we take mass of the Sun times
0.007 times speed of light squared...
How long can the sun shine burning Hydrogen?