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Q & A: Atomic mass numbers not integers

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Most recent answer: 10/22/2007
Q:
why the relative atomic mass number is never a whole number
- brendan
Madras College, Scotland
A:
Good observation! This is a really important question with three contributions.

Most periodic tables give the masses of atoms in "Atomic Mass Units", or AMU. One AMU is 1/12th the mass of a Carbon-12 atom. But the masses listed (at least in the periodic table on my bookshelf) are not for any particular atom, but for an average over the naturally-occurring isotopes, taking their natural abundances into account. An isotope of a chemical element is defined to be an atom with the same number of protons (and therefore electrons, if it's not ionized), and a different number of neutrons -- each possible number of neutrons in an atom corresponds to a different isotope. Because most atoms with several stable isotopes have natural abundances that are shared in some fractional way between the possible isotopes, you will get fractional masses.

Another very interesting effect is that the mass of an atom corresponds to the total energy of everything inside. A big piece of this energy is in fact negative -- it's the potential energy of the forces which bind the protons and neutrons together. Pull a nucleus apart into its component protons and neutrons, add up all the masses you get, and you will have more than if all the protons and neutrons were stuck together. This is so because you have to add energy to pull a nucleus apart, and E=mc^2. The binding energy contributes to the fractional masses of atoms. Furthermore, the electrons and their kinetic and binding energies also contribute to the total mass of an atom.

Another effect is that a proton and a neutron have slightly different masses. The mass of Carbon-12 and Boron-12, for example, will be different because Boron-12 has one more neutron, and one fewer proton and one fewer electron. A free neutron will in fact decay into a proton and an electron and an electron antineutrino, so it has more mass, and enough to give the electron and neutrino some kinetic energy in the decay. A neutron bound in a stable nucleus cannot decay in this manner because the decay of a neutron into a proton changes the binding energy of the nucleus by more than what you get by turning the neutron into a less massive proton (minus the minimum energy needed to create the electron and neutrino).

Tom

(published on 10/22/2007)

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