I am looking at a table of the atomic masses of atoms here. The precision of these measurements astounds me.
The mass of an electron being 1/1800 that of a proton or neutron would certainly make a difference in most of these numbers but students are taught that the electrons do not contribute significantly to the mass.
I suppose for anything but the most analytic of chemistry labs, they do not make a difference but they must be a part of the chart above.
Am I correct?
As mentioned in the “cookbook fractions” thread, it is a matter of significant digits. For most applications, it doesn’t really matter that the mass of a mole of an atom is 10.001 grams instead of 10 grams. The difference in accounting for different isotope mass swamps any accounting for election mass. (A sample of element x might have some atoms with 7 neutrons, some with 8 neutrons, some with 9 neutrons, etc.)
As I recall, some of these calculations assume that a proton and a neutron have the same mass, which is a bigger error than assuming that the electrons are massless.
You can measure atomic masses precisely enough for the electrons to matter, and laboratories dedicated to ultra-precise measurements often do so. But despite the fact that you can, such ultra-precise measurements are almost never needed or relevant.
The atomic mass unit is defined as 1/12 the mass of carbon 12. (It used to be 1/18 the mass of oxygen which had a mixture of various isotopes.) So in the definition isotope differences don’t matter. But yes it makes negligible difference for most purposes.
I can think of one situation where the electron masses do matter. Some radioactive isotopes can decay via “positron emission”, in which a proton turns into a neutron, emitting an anti-electron. These same isotopes can also undergo “electron capture”, where an electron that was orbiting the atom combines with a proton to form a neutron. The daughter isotope that is left over after the decay is the same in both cases, and both cases, the energy that is released in the decay is given by the difference in mass (before & after) times c[sup]2[/sup].
However, if you count the electrons carefully, the mass that remains after the positron emission process is greater than the mass remaining after the electron capture process, to the tune of 2 electron masses. In particular, this means that any isotope that can decay via positron emission can also decay via electron capture. But the reverse is not true, since it’s possible to have a situation where the daughter nucleus is lighter than the parent nucleus, but the daughter nucleus plus two electrons is more massive than the parent nucleus.
An example of this is Beryllium-7. It would “like” to decay into Lithium-7, but the mass difference between these two isotopes is so small that it can only do so if it absorbs one of its orbiting electrons. This means that if you strip away all the electrons surrounding it (as can happen in high-energy cosmic rays), the nucleus becomes stable.
I knew a Physicist who was really into calculating the mass of low mass isotopes. Hydrogen, Deuterium, etc. He had numbers to insane number of digits.
I’ve long considered 9 digits “good enough for reality”. That was double precision way back when. At ten digits it’s like measuring atoms with a meter rule. 9 digits was just a start for this guy.
The mass of an electron would be a very big number from that point of view.
The key point was to compare theory and experimental results. If you find a discrepancy maybe there’s an effect that no one’s noticed before and you could be onto something big, in a very small way.
Keep in mind the excess precession of Mercury’s orbit was an anomaly until General Relativity.
I knew a physicist like that, too, except with calculations for more complex molecules. He compared it to finding the weight of the captain of a battleship by weighing the battleship with him at the helm, and then again without.
Hence why I said that such precision is almost never needed.
It’s a table for chemistry. In no chemical reaction will a significant number of atoms in the reaction lose or gain electrons that aren’t just handed to another reactant.
That said it’s a silly table showing different types of data in a single column. You’ll note that the most precise data has an asterisk next to it to indicate that it’s the atomic weight of the isotope with the longest half life. (For some reason they haven’t used precise dato for Radon though.) The other masses will be based on the average atomic mass in a sample with the average distribution of isotopes. The precision could indicate something about how much the distribution of isotopes varies, but it looks a lot like this is just a shoddy piece of work.
And on thinking about it some more, MikeS’s example of electron capture still isn’t a counterexample. That’s a case where the precise nuclear mass matters, not one where the precise atomic mass matters. And it’s quite common for precision to be relevant in calculations of nuclear mass, since that determines the energy released (or needed) in nuclear reactions.
I’m not seeing the shoddiness. It’s standard practice on periodic tables to list the average isoptopic masses for naturally occurring elements and to list a single mass for cases where that isn’t possible (e.g., elements for which all the isotopes are short-lived).
As to the inclusion/exclusion of the electron masses: I don’t think it’s been explicitly stated yet that the atomic masses do include the electrons, with the scale set such that the mass of carbon-12 including the six electrons is exactly 12. It’s true that getting this wrong won’t make or break a high school chemistry lab, but it’s relevant in other contexts, and the information on a period table needn’t be limited to what’s applicable to a student lab.
The most “everyday” need for knowing masses well is in mass spectrometry, a technique with broad applications (and through which atomic masses are originally measured). You need to know where your target atoms/molecules will appear in the spectrum, and for heavier molecules you would mischaracterize their atomic content if you forgot to count the electrons. (Consider a protein with hundreds or thousands of atoms.)
I agree, and I’m not a physical chemist, so my opinion can be taken with several grains of salt. I just found the variation in significant digits to be odd. But apparently that is indeed the recognized level of precision known: Standard Atomic Weights | Commission on Isotopic Abundances and Atomic Weights
So all I’m left with then is to wonder why Radon, which gets the asterisk for “longest lived isotope” only gets three significant digits, while Francium gets eight? Now that is not due to available data.
Nobody’s going to be deducing the atomic content for a protein with a mass in the tens of thousands from the mass spectroscopy. You might identify such a molecule using mass spectroscopy, but that’d be through comparing one experimental value to another, and so there wouldn’t even be the opportunity to “fail to account for the electrons”. You probably wouldn’t even use an instrument precise enough there, either: Any additional information you need is going to come not from more digits in the one measurement, but from cutting the protein up in various places and repeating the spectroscopy for those pieces.
I just don’t see the argument. The statement being made in the thread seems to be that you can get away with precision worse than part-per-thousand-ish and that it is silly to put anything that precise on a chart. But if you want to make any sense of the measurements coming out of a mass spec, you need to be working at that level of precision. So the OP’s concern that “students are taught that the electrons do not contribute significantly to the mass” is a valid one in this setting.
The electrons are significant in the sense that a protein molecule without all of its electrons would have a measurably different mass than one with all of its electrons. But there’s no way to get a protein molecule without all of its electrons: It’s not like you can forget to include them when you’re doing a measurement.
The electrons are also significant in that one needs to know whether the convention is to include them or not in tabulated elemental masses. Else, one can’t make absolute interpretations of the measurements. (Relative interpretations are fine, as you have noted.)
But my contention is that “absolute interpretations of the measurements”, in the sense you’re describing, simply aren’t done in the first place.
Tables like this one here serve as the references you are describing, but those numbers aren’t magic numbers. They are masses that include the electrons, so someone wanting to understand or calculate the numerical values or their differences based on the corresponding chemical formulas needs to understand the conventions used. Sure, someone’s done the hard work of building all these reference tables, so someone else could treat them as magic, but that’s no way to operate.
Pasta is correct - these measurements are important and they’re actually done every day. If you make a new chemical compound that has never been made before [not an unusual occurrence given the vastness of chemical space], you need to provide certain characterisation data in order to publish it - to prove it is what you say it is. One such datum is proof of empirical formulae, which is considered to be the most fundamental characteristic of any new compound.
The easiest way of doing this nowadays is a high resolution mass measurement (although there are other methods). For the organic compounds I work with, MW typically between 100 and 1000, the accepted error is +/- 5 ppm.