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How do we measure the number of protons, electrons, and neutrons inside an atom? What experiments can be conducted to determine, for example, that an iron atom contains 26 protons?

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  • $\begingroup$ We do not measure the number of protons, electrons, and neutrons inside an atom. If you know it's an atom of iron then there's hardly a reason to reinvent a wheel. If it was an unknown atom, then still identification that it's iron or something else would be simplest. $\endgroup$
    – Mithoron
    Sep 29, 2023 at 12:26
  • $\begingroup$ If for some reason you wanted to waste you're time on that, then you could completely strip your atom of electrons and measure the charge of the nucleus - if its 26 times higher then elementary charge, than there's 26 protons. Unless you somehow doubt the value of the charge of proton? $\endgroup$
    – Mithoron
    Sep 29, 2023 at 12:30
  • $\begingroup$ This is a whimsical suggestion to even think of stripping all electrons of an element to determine the number of protons in iron! $\endgroup$
    – AChem
    Sep 29, 2023 at 12:34
  • $\begingroup$ @AChem In accelerators it's done all the time. Mass and charge can be measured pretty easily from behaviour or the nucleus in the magnetic field. Obviously it's not a "chemical" method, but I already mentioned chemists don't measure such things. $\endgroup$
    – Mithoron
    Sep 29, 2023 at 13:27
  • $\begingroup$ The number of protons, neutrons, and electrons in most of the natural elements were indirectly deduced long before accelerators were used to create new elements. $\endgroup$
    – AChem
    Sep 29, 2023 at 15:15

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There are no techniques that directly count the number of electrons, protons and neutrons in an atom. All deductions about basic atomic structure were established indirectly, well before the 1940s with the help of chemical properties and purely chemical measurements of atomic weights. No machines needed except a highly accurate mass balance. One would determine the atomic weight of iron from quantitative chemical reactions.

It will not be wrong to say that it was purely the empirical periodic table led to our basic conceptions about the atomic structure. None of the fancy techniques mentioned in the other answer such energy dispersive X-ray spectroscopy or particle induced X-ray emission were there to count or probe the atomic structure. These are analytical techniques and need calibration, i.e., someone has to tell the instrument that this frequency is associated with a certain element.

Chemists had already deduced chemical properties and arranged them in a "periodic" table showing that chemical properties repeat periodically like periodic mathematical functions more than 100 years ago. The chemical elements, then known, were also roughly arranged according to the atomic weight (or atomic mass today) not by atomic numbers as done today. Physicists started to probe this arrangement deeper and deeper and this is where X-rays started to help explain this periodic phenomenon of chemical properties.

It was young Moseley's X-ray work that established that the ordinal number of the elements (let us call it $Z$) in the periodic table was related to frequency of the X-rays emitted by each element. Since Bohr had established that hydrogen has a Z=1 with one proton, it was Moseley's intuition that led to the proton count of the elements.

By electrostatic theory, the positive charge must be balanced by negative charges. So the number of protons must equal the number of electrons. The last question is number of neutrons: The number is neutrons was deduced, again indirectly, from atomic masses because the mass of the protons did not add up to the atomic mass. Something "else" was there, and this was the mass of neutrons. Mass spectrometry also established isotopes.

So back to your original query: How do we know that iron has 26 protons...it is because of Moseley's law.

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    $\begingroup$ This is a useful answer, but the OP does not explicitly ask for a historical explanation. Also, intuition is not proof, so one might ask when Moseley's law became a law rather than remained a hunch. $\endgroup$
    – Buck Thorn
    Sep 29, 2023 at 8:29
  • $\begingroup$ @BuckThorn, If the OP knew the history he/she would not have asked this question. $\endgroup$
    – AChem
    Sep 29, 2023 at 12:30
  • $\begingroup$ Again, I do not mean to suggest that your post is invalid. My point is simply that the OP posed a broad question that does not imply a desire for an answer describing how these properties were originally determined. There are now other tools available. $\endgroup$
    – Buck Thorn
    Sep 29, 2023 at 15:03
  • $\begingroup$ @ Buck Thorn, That is fine what are the other tools that you have in mind that will directly tell us the number of electrons, protons or neutrons from absolute measurements (not by calibration matching of standards). I don't think there are any except ultrahigh resolution mass spectrometers. $\endgroup$
    – AChem
    Sep 29, 2023 at 15:11
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    $\begingroup$ I think X-rays will come to rescue using Moseley's law by pure empirical pseudo ab-initio way, as if we were handling iron for the first time. Second option would laser ablating the sample and doing mass to charge ratio studies of the ions from the new element (iron). $\endgroup$
    – AChem
    Sep 29, 2023 at 15:38

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