Bohr model & relativity on large atoms?

[Ruptor]

Why Doesn't the increase in mass of the electrons, due to the relativistic correction required to prevent the calculated electron speed exceeding the speed of light, increase the mass of the atoms of the large elements? If the electrons were heavier on larger elements then the mass would diverge from the proton/Neutron value wouldn't it?

 

[FeynmanIsCool]

This question is answered by a topic called "Relativistic Quantum Chemistry"
http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry

If you scroll down to the "Qualitative Treatment" section, your question will be answered. By the M_rel and Bohr Radius equations.

 

[Ruptor]

So I guess the relativistic increase in mass of the faster electrons in heavier elements is the reason the atomic masses don't go up in nice multiples of proton+neutron+electron masses in the periodic table.

 

[mfb]

You have to be careful here:

- the Bohr model is good for hydrogen-like atoms only: Atoms with a single electron, and (with additional corrections) electrons with filled shells and a single outer electron.
- relativistic mass is a very problematic concept
- while a captured electron gains some kinetic energy, it loses more potential energy. In total, the system loses energy
- the overall effect on the mass of the combined system (~1MeV/c^2) is still below nuclear binding energies (some MeV/c^2 and nucleon).

 

[FeynmanIsCool]

Your very correct. But it helps to understand the concept, even if its only applicable to H electrons. Relativistic mass in this sense is still problamatic