Why is there variation in atomic weight of elements?

In summary, the weights of elements vary due to the presence of different isotopes, each with their own atomic mass. The atomic weight listed in the periodic table is an average of the different isotopes, reflecting their natural abundance in a sample of that element. The small discrepancies in atomic weight can also be attributed to nuclear binding energy.
  • #1
protonic_mass
16
1
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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
uart said:
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?
 
  • #6
protonic_mass said:
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%.
 
  • #7
protonic_mass said:
<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 [tex]E=mc^2[/tex]. 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.
 
  • #8
protonic_mass said:
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
 
  • #9
protonic_mass said:
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.
 

1. Why do different elements have different atomic weights?

The atomic weight of an element is determined by the number of protons and neutrons in its nucleus. Since different elements have different numbers of protons and neutrons, they will have different atomic weights.

2. How is atomic weight calculated?

The atomic weight of an element is calculated by taking the average mass of all its isotopes, weighted by their relative abundance. Isotopes are atoms of the same element with different numbers of neutrons.

3. Why is atomic weight given as a range?

Atomic weight is given as a range because it can vary slightly due to the presence of different isotopes in nature. For example, carbon has an atomic weight range of 12.0096-12.0116, depending on the abundance of its isotopes.

4. How does atomic weight affect an element's properties?

The atomic weight of an element can influence its physical and chemical properties. For example, elements with higher atomic weights tend to have higher melting and boiling points, and may be more reactive.

5. Can atomic weight change?

The atomic weight of an element is considered a constant value for a specific element. However, it can change in certain situations such as radioactive decay or when an element undergoes a nuclear reaction.

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