How did people determine the proton number for each element from experiment in each decade of 20th century?
Moseley, the physicist who 'fixed' the Periodic Table at the start of the 20th Century, did it by measuring X-ray spectra. The energy of the $K_\alpha$ X-ray emission line is proportional to $(Z^2 - 1)$, where $Z$ is the atomic number.
The results of Moseley's experiment fitted his formula so perfectly that he was able to predict the existence of several as-yet-undiscovered elements by looking at the gaps in his graphs. He also re-ordered the controversial placement of nickel and cobalt. Sadly he was killed in World War One before he was able to become the great scientific figure he surely would have been.