Bohr model & relativity on large atoms?

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SUMMARY

The discussion addresses the impact of relativistic effects on the mass of electrons in large atoms, specifically within the framework of Relativistic Quantum Chemistry. It concludes that the relativistic increase in electron mass does not lead to a proportional increase in atomic mass due to the interplay of kinetic and potential energy, which results in a net energy loss for the system. The Bohr model is identified as applicable primarily to hydrogen-like atoms, emphasizing the limitations of using relativistic mass in this context.

PREREQUISITES
  • Understanding of Relativistic Quantum Chemistry
  • Familiarity with the Bohr model of the atom
  • Knowledge of kinetic and potential energy concepts
  • Basic grasp of atomic structure and binding energies
NEXT STEPS
  • Research the principles of Relativistic Quantum Chemistry
  • Study the limitations and applications of the Bohr model
  • Explore the relationship between kinetic and potential energy in atomic systems
  • Investigate nuclear binding energies and their implications for atomic mass
USEFUL FOR

Physicists, chemists, and students of quantum mechanics seeking to understand the effects of relativity on atomic structure, particularly in heavy elements.

Ruptor
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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?
 
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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.
 
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).
 
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
 

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