# Why is there variation in atomic weight of elements?

#### protonic_mass

I am trying to find a clear answer as to why elements' weights vary, when their makeup are of the same protons, electrons, and neutrons?

For example, H = 1.0079 atomic weight, 1 proton + 1 electron
Li = 6.941 atomic weight, 3 protons + 3 electrons + 4 neutrons

If a neutron = 1 proton + 1 electron in the nucleus, then Shouldn't Li be cluster to 7.0553 atomic weight?

Related Other Physics Topics News on Phys.org

#### Janus

Staff Emeritus
Gold Member
The quick and dirty answer is that any element comes in different isotopes, meaning that there can be a variation of the number of neutrons. A sample of any given element will have a mix of isotopes. The atomic weight is the average for a typical sample of that element.

#### uart

Hi Protonic, there are two reason for atomic mass "discrepancies", one small and one much larger.

The small one is of course the nuclear binding energy. For stable isotopes the mass of the nucleus is less the sum of the mass of it's constituent nucleons by an amount equal to the binding energy (divide c^2).

The big "discrepancy" however is simply due to isotope ratios. That is, the atomic mass listed in the periodic table is the average over the stable isotopes of that element in the ratios that they are found in nature.

For example with Li, it occurs in nature as Li7 and Li6 isotopes in the ratio of about 92.5% and 7.5% respectively. The listed atomic mass simply reflects the weighted average of these two isotopes.

#### gmax137

By the way, that is an excellent question, and it probably bothered/confused a number of physicists & chemists in the days when such measurements were possible, but before the explanation (varying number of neutrons in the nucleus) was figured out.

#### protonic_mass

The small one is of course the nuclear binding energy. For stable isotopes the mass of the nucleus is less the sum of the mass of it's constituent nucleons by an amount equal to the binding energy (divide c^2).
Would you elaborate on this? I am looking at the very small variation. If the average of the isotopes is the case, why would they publish the periodic table of elements with averaged weights, and not weights that were derived from the absolute atomic weights of protons, electrons and neutrons? For instance, why publish that Li is 6.941 and not 7.0553?

#### Nabeshin

Would you elaborate on this? I am looking at the very small variation. If the average of the isotopes is the case, why would they publish the periodic table of elements with averaged weights, and not weights that were derived from the absolute atomic weights of protons, electrons and neutrons? For instance, why publish that Li is 6.941 and not 7.0553?
Because then you have to specify the isotope you're talking about, and it's much more convenient to use an average. For example, if I take a sample of raw lithium, in your case, it's not going to be 100% one isotope. So, the value for only one isotope isn't going to help me much because my sample is not pure. Convention, but it's probably more useful than simply stating the masses for each isotope.

As far as the binding energy is concerned, it comes from general relativity that for a stable bound nucleus, the mass of the constituents is less than the mass of the whole. For example, Helium, with 2 protons and 2 neutrons, has a mass less than the mass of 2 protons and 2 neutrons. It's usually pretty small, on the order of 1 MeV. Considering that the mass of nucleons (protons and neutrons) are on the order of 1 GeV, the effect is usually less than .1%.

#### Cantab Morgan

<cut> why would they publish the periodic table of elements with averaged weights, and not weights that were derived from the absolute atomic weights of protons, electrons and neutrons? <cut>
Your phrase "absolute atomic weights of protons..." raises a red flag. Take care that you are understanding what has been written about binding energies. Remember $$E=mc^2$$. If you could "weigh" a lone neutron and a lone proton, their sum would not equal the "weight" of a deuteron.

It's very counter-intuitive, but masses don't add.

#### Janus

Staff Emeritus
Gold Member
Would you elaborate on this? I am looking at the very small variation. If the average of the isotopes is the case, why would they publish the periodic table of elements with averaged weights, and not weights that were derived from the absolute atomic weights of protons, electrons and neutrons? For instance, why publish that Li is 6.941 and not 7.0553?
Atomic weight is a dimensionless physical quantity and is calibrated by defining the atomic weight of Carbon 12 (6 protons and 6 neutrons) as being exactly 12. It is a ratio for a representative sample of an element. An example is Chlorine, which can have either 18 or 20 neutrons. In a representative sample, there is 75.4% of one and 24.6% of the other, and thus Chlorine has an atomic weight of 35.457.

The "atomic mass number", OTOH, is the number of nucleons in the nucleus of an isotope, thus you can have Carbon 12 or Carbon 14 for example, or Hydrogen 1, Hydrogen 2 or Hydrogen 3

#### alxm

Would you elaborate on this? I am looking at the very small variation. If the average of the isotopes is the case, why would they publish the periodic table of elements with averaged weights, and not weights that were derived from the absolute atomic weights of protons, electrons and neutrons? For instance, why publish that Li is 6.941 and not 7.0553?
Uh? Because that would be totally useless for 99% of all chemistry, which rarely ever deals with any substances that have anything other than the natural distribution of isotopes, except in the specific cases of using it for "isotope labeling" purposes.

Isotopes have no unique chemical properties bar one (kinetics). So they're not interesting. For the same reasons, isotope enrichment is difficult and very expensive.

So why, would you ever print an atomic weight that was not a average of isotope weights, weighted by natural abundance? It'd make life harder for everybody.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving