For such a simple question, I cannot find an answer anywhere. Are the energy levels specific to each atom? For example, is the energy required to jump from the first energy level to the second energy level of Boron the same in each atom? Or are energy levels different for every single atom (even ones with the same proton number)?

Sorry if this is a stupid question, I'm fairly new to energy levels in physics.

  • 3
    $\begingroup$ The energy levels are different in each type of atom. See e.g. hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.html#c1 and how they differ from hydrogen. $\endgroup$
    – Gert
    Oct 11, 2015 at 19:04
  • $\begingroup$ This is how astronomers are able to tell what element is present in the relevant spectra. $\endgroup$
    – Kyle Kanos
    Oct 11, 2015 at 19:08
  • $\begingroup$ And everyone else here on Earth doing spectroscopy... $\endgroup$
    – Jon Custer
    Oct 11, 2015 at 19:09
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    $\begingroup$ ... but every Boron atom has the same energy levels $\endgroup$
    – garyp
    Oct 11, 2015 at 20:52
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    $\begingroup$ Every 10-boron atom has the same energy level. Those of 11-boron are shifted (due to the slightly different reduced mass). $\endgroup$ Oct 11, 2015 at 22:14

1 Answer 1


Short/practical answer: Energy level structure is in a practical way, specific for atomic species. e.g. all Boron atoms have the same energy level structure. This is why spectroscopy works.
Long/theoretical answer: You need to specify the exact Hamiltonian of the system to do that calculation. When you do that, ionic species are slighty different in energy levels compared to neutral species due exchange interaction and total coulombian interaction, and isotopes have slighty differente energy levels due a negligible term of gravitational energy contribution because nucleus mass is different and also because reduced mass of system is changed (reduced mass as pointed @Sebastian Riese, when reduced mass is greater than another specie is near to Bohr-Oppenheimer approximation where nucleous is static).
Thus, energy levels are different in ionic and isotopes species of the same atomic number.


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