eli5 why do some elements on the periodic table have atomic weights with decimals and others don’t?

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All elements and isotopes will have an atomic mass with decimals except for Carbon-12. The definition of an atomic mass unit is 1/12 of the mass of a free carbon-12 atom.

The mass of a free proton and neutrons is just above 1, the mass will decrease if you them both together because some are lost in the binding energy between them. So the atomic mass is very close to the total number of protons and neutrons but not exactly except for C-12.

The value you see with be the average atomic weight of an atom when found on Earth. For chlorine that is 35.45u The reason is there are two stable isotopes that make up practically all of it found on Earth. It is 76% Cl-35 and 24% Cl-37 and if we just use those we get 0.76* 35 + 0.24*37= 35.48u which is quite close 35.45u.

Even carbon has a listed decimal mass of 12.011u. The reason is carbon-13 is also stable and makes up 1.06% of all carbon Earth.

This is the reason you find atomic masses that is not close to integers, there are multiple stable and common isotopes on earth

The calculated chlorine atomic mass is 0.02u to high because the masses are not exactly 35u and 37u but 34.96885269u and 36.96590258u. The normal proportion is more exactly 0.7576 and 0.2424. If we use that number we get 35.452937583336. I used just the number of nucleons to show that multiple isotopes are the main reason the mass is far away from an integer.

The percentage is still a bit of a simplification because it can vary and a range of 0.75644–0.75923 is possible and result in an average mass range of 35.4497 to 35.4553. We can measure the isotope mass very accurately bit that does not help if there is variation in the proportions you find and it limits the accuracy of the value.

Then is the question what number do you put for element that you do not find on Earth to any significant degree? You can pick the mass of the issues with the longest half-life or like on https://en.wikipedia.org/wiki/Periodic_table just list the atomic number of the most stable isotope in []. If you look at element 87 Francium Wikipedia shows [223] that it is the most stable isotope even if it mass is 223.0197359

https://en.wikipedia.org/wiki/Isotopes_of_francium

If you see integer values for elements that exist on Earth like 14 for Nitogren. The answer is then the accuracy is just 1 decimal and round from 14.007u

Lots of good insights here. At a higher level I’d add that numbers/quanta are inherently ‘imperfect or imprecise’ as it relates to explaining most fundamental physical/natural concepts, e.g., π going on ‘forever’. They’re an applied science (and the best we can do within the limits of our understanding).

Isotopes. Example: Copper is about 69% Cu63, and 31% Cu65 (with miniscule amounts of others. So copper’s atomic weight is .69x 63 + 31%x 65.

For most elements, the atomic weight given is the weighted average of all of that element’s isotopes. There is also a small deviation from a whole number in most isotopes because protons and neutrons don’t have exactly the same mass, and because of something called nuclear binding energy.

For radioactive elements, however the given weight is just the mass number (number of protons + number of neutrons) of whichever isotope has the longest half-life.